A resumptive expression is one that occurs in where a trace should have been. This strategy is widely used by languages to salvage constructions in which movement is expected but is ungrammatical for various reasons.
Here is an example:
1. *This is the guy that after you talked to XX everyone got very upset.
2. This is the guy that after you talked to him everyone got very upset.
Many native speakers of English find (2) better than (1). You can see from these examples that when a gap (marked as XX) is unacceptable, a pronoun in the position of the gap may help salvage the sentence. This use of the pronoun is called a resumptive.