Phase is the offset of two waveforms expressed in degrees, where 360 degrees corresponds to a delay of one cycle. Waveforms that are 180 degrees out of phase will cancel each other out to complete silence.

Phase problems can occur when two similar sound sources are out of alignment with each other. This causes the drop out of certain frequencies, which can make recordings sound thin if not dealt with.

Diagram visually explaining phase
Phase issues need to be taken into consideration any time you are recording more than one version of the same sound source. Examples of this would be recording a drumkit with multiple mics, or else recording a bass guitar with both a DI box and miked up amplifier. Careful mic placement can help in both cases.