<security> (Or "login", "log on", "logon") To start a session with a system, usually by giving a user name and password as a means of user authentication. The term is also used to mean the ability to access a service (also called an account), e.g. "Have you been given a login yet?"
"Log in/on" is occasionally misused to refer to starting a session where no authorisation is involved, or to access where there is no session involved. E.g. "Log on to our Web site!"
The noun forms are usually written as a single word whereas the verb forms are often written as two words.
To end a session is to "log out" or "off".