A vector space contains a collection of objects called vectors which are numerical representations of words, sentence, and even documents. While a simple vector like map coordinates only has two dimensions, those used in natural language processing can have thousands.
The vector space model is an algebraic model that represents objects (like text) as vectors. This makes it easy to determine the similarity between words or the relevance between a search query and document. Cosine similarity is often used to determine similarity between vectors.
The vector space model uses linear algebra with non-binary term weights. This means the continuous degree of similarity between two objects, like a query and documents, can be calculated allowing for partial matching.