A session is a gathering. A court or other assembly is said to be in session when they convene.
In computing, in particular networking a session is either a lasting connection using the session layer of a network protocol or a lasting connection between a user (or user agent) and a peer, typically a server, usually involving the exchange of many packets between the user's computer and the server. A session is typically implemented as a layer in a network protocol (e.g. telnet, FTP).
In the case of transport protocols which do not implement a formal session layer (e.g. UDP) or where sessions at the session layer are generally very short-lived (e.g. HTTP), sessions are maintained by a higher level program using a method defined in the data being exchanged. For example, an HTTP exchange between a browser and a remote host may include a HTTP cookie which identifies state, such as a unique session ID, information about the user's preferences or authorisation level, etc.
See in this context also login.