An extensional definition gives the meaning of a term by listing everything in its extension -- that is, everything that falls under that definition. An extensional definition of "nation" would be all the nations in the world; an extensional definition of "ocean" would be pointing out all the oceans. An extensional definition of "person" would be every person who ever lived -- as might be clear, extensional definitions are best used for small sets, and impossible for infinite ones.
Extensional definitions are used when listing examples would give more applicable information than other types of definition, and where listing the members of a set tells the questioner enough about the nature of that set.
This is similar to an ostensive definition, in which one or more members of a set (but not necessarily all) are pointed out as examples. The opposite approach is the intensional definition, which defines by listing properties that a thing must have in order to be part of the set captured by the definition.
See also: extension (semantics).