A phaser (also known as phase shifter) is a type of modulated delay where an audio signal is split into two paths. One path is treated with an all-pass filter, which preserves the amplitude of the original signal and alters the phase. The amount of change in phase depends on the frequency. When signals from the two paths are mixed, the frequencies that are out of phase will cancel each other out, creating the phaser's characteristic notches. Changing the mix ratio changes the depth of the notches; the deepest notches occur when the mix ratio is 50%. 
The definition of phaser typically excludes such devices where the all-pass section is a delay line; such a device is called a flanger.
Comparison of common modulated effects
(this section is copied from another article)
The similarities and differences between the common modulated effects (flanger, chorus, phaser) are summarized below:
- Flanger has the strongest and most noticeable effect. Chorus is more subtle. Phasers are subtler still.
- Flanger and chorus effects create delayed copies of the original signal and mix them back. Phasers use a series of all-pass filters to create phase shifts at various frequencies.
- Flanger uses shorter delay times (<7ms) than chorus (<20ms).
- Phasing can be used in a similar way to chorus, but, whereas chorus creates the impression of two slightly detuned instruments playing the same part, phasing sounds more like a single sound source being filtered. 
- Chorus (typically) is not fed back, whereas flangers often are.
- Phasing and flanging both produce comb filters. However, in flangers, the individual notches are linearly spaced. In phasers, they are uneven. 
- Flangers sound more pronounced and natural than phasers (like the jet plane "whoosh" effect), whereas phasers tend to sound more subtle and "otherworldly". 
- Dry/Wet - Adjusts the balance between the processed and dry signals. Set to 100% if using a phaser on a return track.
- Poles/Stages - Determines the number of notches/peaks in the sound, affecting the general sound character.
- Feedback - The amount of signal from the all-pass chain that is fed back into the input.
- LFO Controls - If a phaser has a set of LFO controls, they are used to modulate the filter frequency over time.
- Frequency - Represents the frequency where the phase shift is at 180 degrees. The comb filter produced by a phaser is mildly windowed around this frequency. 
Try using triangle shaped LFOs on modulated effects such as flangers, phasers, and chorus. With sine waves and other LFO types, there is a often an unnatural "stall". 
Adding feedback to the effect accentuates the peaks (or poles) of the resulting comb filter, and rounds out the notches.
A phaser is sometimes used to make a sound appear as if it was synthetically generated, like turning a natural human voice into a computer or robot voice. The technique works because the frequency filtering produces sound commonly associated with mechanical sources, which only generate specific frequencies, rather than natural sources, which produce a range of frequencies. A vocoder is a different effect used for similar purposes.