What are the differences between the four types of cadence?

A perfect cadence is chords V-I. When there is a perfect cadence the music sounds finished.

An imperfect cadence is any chord moving to V (e.g. I-V, II-V, IV-V). The music does not sound finished.

An interrupted cadence is chords V-VI. These chords sound as though they are about to be a perfect cadence (i.e. end up on chord I) but end up moving to chord VI. 

A plagal cadence is chords IV-I. It is known as sounding like an 'Amen' chord due to its prominence in religious choral music.