Much like optical illusions, auditory illusions are sensorial ambiguities. Your ears (and your brain) can trick you into hearing what isn't. Or they can distort pitches (frequencies), textures, dynamics, spatial location of sound sources, etc.
Auditory illusions may be related to psychoacoustic (see Shepard's tone scale) or physical phenomena (see Doppler effect).
These paradoxes may be designed simply to astonish or as an artistic mean, but have also scientific applications: eg. for electroacoustic techniques or medicine (tinnitus research).
They also occur in everyday life (eg. exaggerated perception of concerthall dynamics compared to recordings). Even the stereo effect can be considered an auditory illusion of spatialness.
Besides the mentioned, some interesting examples are: