I heard that Subversion is an Apache extension. What does it use for servers?

No, Subversion is a set of libraries. It comes with a command-line client that uses them.

There are two different Subversion server processes: either svnserve, which is small standalone program similar to cvs pserver, or Apache httpd-2.0 using a special mod_dav_svn module. svnserve speaks a custom protocol, while mod_dav_svn uses WebDAV as its network protocol. See chapter 6 in the Subversion book to learn more.