Vector Space Models of Semantics
The idea of the VSM is to represent each document in a collection as a point in a space (a vector in a vector space). Points that are close together in this space are semantically similar and points that are far apart are semantically distant.
The user's query is represented as a point in the same space as the documents (the query is a pseudo-document). The documents are sorted in order of increasing distance (decreasing semantic similarity) from the query and then presented to the user.