A comb filter adds a delayed copy of a signal to itself. Constructive and destructive interference create periodic peaks and notches in the frequency response — like the teeth of a comb.
Feedforward: y[n] = x[n] + g·x[n−D]
Feedback: y[n] = x[n] + g·y[n−D]
D = τ·fs, Notch at f = 1/(2τ) + k/(τ)
Flanging is a comb filter with slowly varying delay (τ sweeping). Chorus uses multiple slightly detuned delays. Room echoes are natural feedback comb filters. Karplus-Strong synthesis uses a feedback comb to simulate a plucked string.