Subversion is a versionning tool: A way to control the evolution of a
software:

I. The main repository (data folder) is centralized in a remote server
for example, and to modify a file you have to make a checkout (a
download), then after editing that file (or multiple files) you make a
commit (upload to the server) and write if you want a comment
describing the modif. This way of working allows a Full Time Tracking
(You can revert any modification).

II. It allows also to work in a collaborative way: If two people work
on the same file, you will be able to see the comments of each others
and if you are working on distinct parts of the file you could make a
merge  with the remote version.

Conclusion: SVN is good as a backup solution and as a collaborative
Platform. (It could also be a solution for publishing the staff if you
are working on a web project).

III. Practically:

1. Create  a repository (folder) in a server where svn (tigris
product) is already installed.
2. Make a checkout of the folder (checkout or co)
3. Work on the local files
4. When you make considerable (relative to projects) modif, make a
commit (commit or ci), then you will be asked to give a comment or: ci
-m "This is a comment" (to commit it out in a single line).
5. Many use tricks exists: For example: SVN supports some config files
where you can prohibit particular files (large one, log files, files
which behaves differently in the server and in the localhost:
database.yml for Railers ;) ) from being committed even when modified.

And for the exact commands and their syntax, there is a great pdf in
the tigris svn website.

Feel free to ask for more details :)