Reverb is the persistence of sound after the sound is produced. It is created when a sound or signal is reflected off of a surface (usually the walls of a room), causing a large number of reflections to build up and then decay as the sound is absorbed by objects in the space, which could include furniture, people, and air.  As time passes, the amplitude of the reflections gradually reduces to non-noticeable levels. Reverberation is not limited to indoor spaces as it exists in forests and other outdoor environments where reflection exists.
In comparison to a distinct delay (echo) that is detectable at around 50-100 ms after the previous sound, reverb is the occurence of reflections that arrive in a sequence of less than approximately 50 ms .
Reverberation occurs naturally when a person sings, talks, or plays an instrument in a performance space with sound-reflective surfaces. However, in music production, reverb is often added electronically to the vocals of singers and to other instruments and sounds.
Below is a list of common ones, but individual plugins will vary widely.
- Wet/Dry - the balance between the processed and dry signals
- Decay Time - a measure of the time required for the sounds to "fade away" in an enclosed area after the source of the sound has stopped. Technically, the reverb time is commonly measured in terms of T60, which refers to the time it takes for the sound pressure level to reduce by 60 dB.  This setting is often used in conjunction with room size (i.e. longer decay times match larger room sizes)
- Room Size - larger sizes typically correlate to longer reverb times and possibly a wider stereo image. As even synthetic rooms can have standing waves, if the reverb sound has flutter (a periodic warbling effect), vary this parameter in conjunction with decay time for a smoother sound. 
- Pre-Delay - sets the amount of time that passes before the first onset of reverb is heard
- Early Reflections Level - sets the level of the first group of echoes that occurs when sound waves hit walls, ceilings, etc. These reflections tend to be more defined and sound more like “echo” than “reverb.” Prominent early reflections tend to work better with sustained sounds, such as vocals and pads, then percussive sounds. Balance the early reflections so they are neither obvious discrete echoes, nor masked by the decay. Lowering the early reflections level also places the listener further back in the room, and more toward the middle. 
- Diffusion - diffusion refers to how close together reflections are. Higher diffusion means a thicker sound, and low diffusion can create more discrete echoes. For percussive instruments, lots of diffusion avoids the “marbles bouncing on a steel plate” effect caused by too many discrete echoes. However, for vocals and other sustained sounds, reduced diffusion can give smooth reverberation that doesn’t overpower the source and maintains clarity.
- EQ - many reverb units have the ability to apply EQ to the final output and/or to filter the input signal before the reverb is applied
- Damping - with softer surfaces (e.g., a hall packed with people), the reverb tails will lose high frequencies as they bounce around, producing a warmer sound with less “edge.” This is known as damping. Damping affects overall tone, so setting it “oppositely” often works well (lots of damping with a bright-sounding song to warm it up, little damping if the song needs more “air”). 
- Low frequency cutoff - any frequencies below this cutoff with follow the decay curve for 'low' frequencies
- Low frequency decay time - how low frequencies decay relative to the overall decay (in most real rooms, the high frequencies will decay faster than the low ones)
- Density - some plugins allow the user the control how dense the early and late reflections are
- Modulation - to create more variation in reverb sounds, modulation adds subtle changes to the reverb characteristics. Increase modulation depth if the reverb sound needs more “animation.”
Types of Reverb
The most basic type of reverb is room reverb, which refers to and mimics any of the diverse set of possible performance areas for sound, including living rooms, garages, and clubs. These spaces can sound totally different and often contain many "imperfections" in, but those imperfections give room reverb it's charm.
Rooms give a natural color and liveliness to a sound. They also sound like a more intimate space and can give the impression that all of the music is being played right in front of you. When going for a natural, in-person, live kind of sound, room reverb is a good choice. 
Concert halls are spaces that are dedicated to the enjoyment of music. As such, they're built to have minimal negative reflections and to sound as tonally even as possible. They are also built to help propagate sound, which is why many halls are bow shaped. 
Big, rich and warm sound are recognizable characteristics of Hall reverbs. They are often favored for their ability to model large physical spaces.
Compared to hall reverb, chamber reverb is on the opposite end of the spectrum. The name "chamber" refers to the reverb chambers that studio owners and record producers would set up in lieue of recording in a giant hall. Smaller rooms were set up with very reflective surfaces and preferably oblong angles. Sounds were played at one end of the room and microphones captured the result at the other end.
Because these rooms were small and full of dense echoes, they had distinct color and texture. Chambers were largely used on older R&B and Classic Rock records and are often used to provide a distinct bump in energy or extra texture. 
Plate reverb is a man-made device that vibrates a sheet of metal when a sound activates the surface. Contrary to in a three-dimensional space, where there are discrete echoes at the front of the reverb tail and as the reverb tails out the echo density increases; in a two-dimensional metal sheet, the echoes are the same density from the start of reverberation to the end. 
Additionally, because the speed of sound if faster in metal than air, plates have a higher echo density. This helps give plates their signature "smooth" reverb tails.
Lastly, the higher frequency tons exhaust their energy much faster than lower tones, while lower tones take longer to build up. This creates the effect of higher frequencies living at the front of the reverb tail while lower frequencies tail out later on. 
Plate reverbs were famous in the '60s, and are still widely used today. They are known to work well with vocals and drums in particular.
Ambience is created using algorithms - there aren't any physical spaces that correlate with the sound of ambience reverbs. Instead, ambience creates an ambiguous space around a sound. The key characteristic of ambience is that it is indistinct and often beyond recognition (i.e. the dry signal loses its original character). Beyond that, ambient reverb could take many forms. 
Perhaps unsurprisingly, ambient reverb is a key component of ambient music and passages. But shorter ambience can also be used to give sounds a sense of three-dimensionality while still sounding relatively dry.
Convolution reverb uses a recorded sample, called an impulse response (IR), that captures the reverberant behavior of a particular space. Convolution reverb units use various IRs to faithfully recreate the reverb at the microphone's position when the IR was made. Sometimes these are referred to as sampling reverbs but there's no sampling involved as such, even though the process seems akin to sampling the sonic signature of a room, hall or other space. 
Because IRs can be recorded in virtually any space, convolution reverbs generally come with a library of IRs ranging from small live rooms to famous venues, top studio rooms, forests, canyons, railway stations and just about anything else you can think of. They sound very convincing, and there's plenty of variety to be had, but once the IR is loaded, there's only a limited amount of editing you can do without spoiling the natural sound. Usually you can apply EQ and also change the envelope of the reverb decay to make it shorter, and adding pre-delay is not a problem, but after that you pretty much have to take what you get. Some companies, such as Waves, have managed to create additional controls but, as a rule, the further you move from the original IR, the less natural the end result. 
- Reverb creates a sense of space, but it also increases the perception of distance. If you need something to appear at the front of a mix, a short, bright reverb may be more appropriate than a long, warm reverb 
- If you need to make the reverb sound 'bigger', a pre-delay (a gap between the dry and wet signals) of up to 120ms can help to do this without pushing the sound too far back, or obscuring it. 
- Though reverb increases the sense of stereo width, it dilutes the sense of stereo position. If you want to pinpoint the placement of something in a mix, you should consider using a mono rather than a stereo reverb, and panning this to the same place as the dry sound. 
- Most synthetic reverbs allow you to balance the level of the early reflections and the later, more dense reverb tail. If you want to keep the sense of space but without the reverb tail taking up too much space in your mix, you can increase the early reflection level and reduce the tail level. 
- Don't add much, if any, reverb to low-frequency sounds, such as bass guitar or kick drums. Where you need to add reverb to these sources, short ambient space emulations usually work better than big washy reverbs, which tend to make things sound muddy. Taking this a step further, you can also make a mix sound less congested by EQ'ing some low end out of your reverbs.