A chaperon is usually a person who is sent over by a third party, to watch over one person or a couple while the observed object(s) is (are) out.
Chaperons were specially popular among parents of teenaged girls during decades gone by. As the modern times (say, 1970s, 1980s, etc.) approached, chaperons became used less and less, until nowadays, the idea of having a chaperon watch over a date could practically be seen as obsolete or un-cool by some teenagers.
Chaperons are still used, however, and some of them perform works that differ from that. For example, a chaperon might go with a group of elders to accompany them during outside activities.
In drama, probably the best known example of a plot revolving around the need for, and lack of, a chaperone is Brandon Thomas's farce Charley's Aunt (1892).