In staggered elections, not all places in an elected body are up for election at the same time. The staggered election keeps some continuity in the elected body.
For example United States Senators have a 6-year term but they are not all elected at the same time. Rather, every two years elections are held for one third of US Senate seats. Elections to the Senates of several other countries, and to regional bodies, are similarly staggered.
Staggered elections should not be confused with rolling election.