This is a rhythm tree. It shows how different notes relate to each other. The whole note at the top of the tree is equally divided into two half notes, or four quarter notes. The names of the notes are the same as common fractions. Therefore, a single sixteenth note at the bottom of the tree is the same as 1/16 of a whole note.
This is the same rhythm tree, but instead of notes (which make sound) we have rests which are silent. The whole rest, like the whole note, is at the top of the tree followed by the half rest, the quarter rest, the eighth rest, and the sixteenth rest.
It is possible to continue this pattern down to thirty-second and sixty-fourth notes/rests but those are less common. While theoretically possible, a 128th note is generally not used in common standardized notation.
Subdivision - To break up a larger metrical pattern into smaller parts so that it may be more easily understood. The division of the beat in simple meter (div. by two) into four equal parts or in compound meter (div. by three) into six equal parts. The division of the beat in simple meter (div. by two) into four equal parts or in compound meter (div. by three) into six equal parts.
Example: You could count 4 quarter notes: 1-2-3-4. Or you could subdivide and count the quarter notes as if they were eighth notes 1 & 2 & 3 & 4 &. This is useful if you want to prepare for upcoming rhythms, or to avoid rushing your part.