In computer sense, A file to which some new information is appended either periodically or when something happens. The information describes the recorded event or transaction in detail. This can be later use to see what happened at specific time in the system or situation. Synonymous with log file, though the word "log" is used more commonly in informal language.
Some examples would include system logs, server logs (such as web server logs), and client logs (such as IRC logs, MUD logs, instant messaging logs, and like).
In Everything2 sense, a log is series of normal nodes that have date in title, used to describe what happened in that day. See day log, dream log, Everything Editor Logs