The classic phaser sound is similar to flanging (in theory, a flanger is really a specific type of phaser). Chorus and flanging both use a simple variable delay that operates uniformly across the entire audio spectrum. Phasing effects - properly called phase shifting - use an allpass filter to delay the signal.
Two things may seem odd about this. Firstly, just as a high-pass filter lets high frequencies pass and a low-pass filter lets low frequencies through, so an allpass filter lets all frequencies pass without attenuation, but what on earth is the point of that? Secondly, why use a seemingly redundant filter as a delay unit?
The answer lies in the fundamental properties of an analogue filter, even one that doesnt actually do any filtering! All filter or equalisation circuits introduce a certain amount of phase distortion. All analogue circuits take some time - usually extremely short - to do their work, and therefore delay the signal slightly. Filters, alongside their main job of cutting or boosting certain frequencies, also delay some frequencies more than others. This distorts the time relationship between the frequencies, which is usually perceived as bad, particularly for stereo imaging, and so high-end equalisers are often sold on the basis of how little phase distortion they introduce.
While phase distortion in mono may have little or no audible effect, mixing the allpass filters output with the dry signal completes the trick. If the delay operates uniformly across the spectrum, then comb filtering occurs - using an allpass filter creates a specific notch or notches depending on the characteristics of the filter. Many phasers, including the classic MXR Phase 90, use several filters in series. An oscillator is used to sweep the notches through the frequency spectrum - the phasers complex sound results partly from applying separate oscillators to each waveform. Most commercial units allow control over only the overall speed of these oscillators.
Phasing can be a hard to describe in words, but its unmistakeable if youve heard it. If youre unsure, listen to David Gilmours intro to the Pink Floyd classic Have A Cigar, or just about the whole of Van Halens first album.