Rests are symbols for writing silence for specific amounts of time. For each durational symbol there is a corresponding rest. In other words, a whole note means a sound should be made for four counts, while a whole rest means to be silent for four counts.

This often makes the most sense when musicians are playing in groups. For instance, during the breakdown in some popular songs, all instruments drop out except for the bass and drums. The remaining instruments (guitars, vocals, etc.) would have rests notated in their music to show how many beats they need to count  before they begin playing again.