In one example, Maryland and Virginia both ceded land in 1790 in order to create what is today the District of Columbia, specified in the U.S. Constitution of the previous year. The Virginia portion was given back in 1847, a process known as retrocession.
Territory can also be ceded for payment, such as in the Louisiana Purchase and Alaska Purchase. Even fraud can be involved, such as in the Treaty of New Echota, whereby lands already taken in 1832 by outright theft of the U.S. state of Georgia were later "ceded" to the state by a Cherokee leader.
A similar concept to cession is concession, while recession is somewhat different.
This is a yielding up, or release. France ceded Louisiana to the United States by the treaty of Paris, of April 30, 1803. Spain made a cession of East and West Florida by the treaty of February 22, 1819. Cessions have been severally made of a part of their territory by New York, Virginia, Massachusetts, Connecticut, South Carolina, North Carolina, and Georgia.