An exclave is a territory that belongs to one state but that its not connected to it, but surrounded by other states. A good example is the region around the Russian city Kaliningrad. It belongs to the Russian Federation, but is separated from the rest of that country by territory belonging to Lithuania, Latvia and Belarus.
An exclave is not necessarily the same as an enclave. The region Kaliningrad is not surrounded by one state only, but by two: Lithuania and Poland and it also borders the Baltic Sea. For it to be an enclave, it would have to be entirely surrounded by one state. Other exclaves that are not enclaves include: the Nakhchivan Autonomous Republic.