A resumptive pronoun is a pronoun in a relative clause

Relative clause

A relative clause is a subordinate clause that modifies a noun phrase, most commonly a noun. For example, the phrase "the man who wasn't there" contains the noun man, which is modified by the relative clause who wasn't there...

which refers to the antecedent of the main (or matrix) clause. The slight majority of world languages use resumptive pronouns instead of gaps in relative clauses. Resumptive pronouns become more common the deeper the relative clause is embedded because of greater processing constraints, even appearing in deeply embedded relative clauses in languages that do not usually allow relative pronouns.

Grammatical for most native English speakers:
I saw the girl that is nice.
I saw the thing that is nice.

Ungrammatical for most native English speakers:
I saw the girl that she is nice.

Marginally grammatical for most native English speakers:
I saw the girl that your friend said that she is nice.

Grammatical for some native English speakers:
Who is the girl that your friend said that she is nice?
Resumptive pronouns in English tend to be disallowed in shallow relative clauses, but required in certain more deeply embedded clauses. For example (where * indicates ungrammaticality):

That's the girl that I like.

*That's the girl that I like her.

*That's the girl that I don't know what did.

That's the girl that I don't know what she did.

Sometimes in cases of deeper embedding, both possibilities are allowed:

This is the boy that, whenever it rains, cries.

This is the boy that, whenever it rains, he cries.