External argument

The external argument of a predicate X is the argument which is not contained in the maximal projection of X. In general, this is the subject of a predicate.

Example
in (i), John is the external argument of the verb buy, and is not part of its maximal projection VP.

(i) John [VP buys books]

An argument of a predicate X which is contained in its maximal projection is called the internal argument. In (i) the NP books is the internal argument of the verb buy.

Link
Utrecht Lexicon of Linguistics

Other languages
German externes Argument