What are the functions of "rests?"

Rests are musical notations that mark a fixed period of silence. The silence, or open space, in a piece of music is equally important to the placement of the notes. A system of carefully placed rests has the ability to make or break a song and to completely alter the its mood or theme. The types of rests and their values mirror that of the notes they are replacing and can be used in a multitude of ways.

Multi-measure rests last for several measures. They are marked as whole rests with the number of silent measures noted above them. Multi-measure rests are typically only used when the piece requires more than eight whole rests in a row.
Four-measure rests last for four measures and are occasionally marked as multi-measure rests. Though it is generally considered more correct to use a multi-measure rest with only eight rested measures, it's not at all uncommon to find four-measure rests marked as such.
Double-whole rests (or breve rests) last twice as long as a whole note. They are represented by a black vertical rectangle between the second and third lines of a musical staff.
Whole rests (or semibreve rests) represent one whole note. This is usually meant as four beats, but whole rests are often used in 3/4 time as well. In this case, whole rests represent a whole measure as opposed to a whole note. They are notated as a black horizontal rectangle under the second line from the top of a staff.
Half rests (or minim rests) are half as long as a whole note. They are represented by a black horizontal rectangle above the third line from the top of a staff.
Quarter rests (or crochet rests) last for a quarter of a whole note. Their notation is the most distinctive and commonly used; it's a nearly indescribable curvy line stretching over the staff's middle three lines.
Rests continue to be notated up to one sixty-fourth of a whole note and can also have their value shifted by placing a dot next to the notation. Dotted rests last the length of the original rest, plus one half. For example, dotted half rests last three beats and dotted quarter rests last one and one-half beats.