A flanger effect pedal doubles your input signal and plays both back together—slightly out of phase and at a slight delay—to produce the signature whooshing sound.
Flanger effects were first achieved by recording a signal onto two separate tape machines at the same time and then manipulating the output of both while recording onto a third machine. The output coming from the two original tape machines would have slight variations in phase, which is essentially what a phase-shifter pedal simulates.
For a flanger effect, the engineer would touch the rim of one of the tape reels (the flange) in increments, which would slow it down and throw the signal out of sync. This is why a flanger effects sounds so much like a phaser, except with that distinct whooshing, comb-filter effect, which is a result of the manipulation of speed in addition to phase.