Basically, the score is a number that represents how well any particular result matches what you searched for.
Here are some more technical details if you were curious: Scoring uses a combination of the Vector Space Model (VSM) of Information Retrieval and the Boolean model to determine how relevant a given Document is to a User's query. The idea behind the VSM is the more times a query term appears in a document relative to the number of times the term appears in all the documents in the collection, the more relevant that document is to the query. It uses the Boolean model to first narrow down the documents that need to be scored based on the use of boolean logic in the Query specification. Lucene also adds some capabilities and refinements to this model to support boolean and fuzzy searching, but it essentially remains a VSM based system at the heart.