Comping is the Jazz term for accompaniment, which includes the art of complementing the soloist with what you play. To do this you need a good knowledge of chords and how to use them, and you must be familiar with Jazz rhythms and approaches to rhythm playing on the Ukulele.
You also need to be a sensitive listener, with the ability to respond quickly to other musicians. This is best developed through a great deal of listening and improvising.
A good way to consolidate your knowledge of note and rest values is to practice them as a set rhythm when playing through a chord progression. This traditional Jazz rhythm pattern is known as "four to the bar", which simply means four quarter note strums per bar. It is a good rhythm to play when learning a new set of chord changes.
Rhythm Pattern