A re-ranker takes a query and a chunk of text and assigns them a relevance score according to how well the text answers the query. (Generally - in theory you could have some other metric of relevance.)

They're called "re"rankers specifically because they're usually downstream of a faster but less accurate relevance algorithm (some kind of full text search and/or vector similarity) in a search pipeline. Rerankers have to run from scratch on every query-document pair and are relatively computationally expensive, and so are practical to run only on a small number of documents.

An "instruction following" reranker basically just has a third input which is intended to be used kind of like a system prompt for an LLM - to provide additional context to all comparisons.

Rerankers are used downstream from an embedding model. Embedding models are "coarse" so they give false positives for things that may not be as relevant as contender text. Re-ranker, ranks bunch of text based on a query in order to find the most relevant ones. You can then take them and feed them as context to some other query.