What is Subversion?
Subversion ("svn") is a version control system; it manages successive revisions of files, keeping track of the latest version of each file, which versions of other files are associated with particular versions of a file, etc. It can be used to:
More SVN info:
The main terms you need to understand are "repository," "revision," and "working copy". The repository is a central store of all the versions of all the files that are under Subversion's control. A revision of the repository is an integer that uniquely identifies the states of all of the files in the repository. A working copy (aka "sandbox") is a local copy of one particular version of one or more files, which you typically edit, test, debug, etc., and then "commit" to Subversion, thereby creating a new revision.
Client/Server Architecture
Subversion has a client/server architecture in which the repository (all the versions of all the files checked into svn) lives on a server, and people access the files via clients.
Basic Work Cycle
Here's some great documentation on the basic Subversion Work Cycle: http://svnbook.red-bean.com/nightly/en/svn-book.html#svn.tour.cycle
To summarize this summary,
You almost never need to refer to the server in a typed svn command, because working copies remember where they came from. So when you say svn update, svn status, svn diff, svn commit, etc., svn automatically interprets these to mean "with respect to the working copy in the current directory and the repository it came from" and so you don't have to mention the server. The only exception is checking out a working copy in the first place; obviously if the working copy doesn't exist yet then you need to tell your svn client which server to get the files from.