Subversion doesn't distinguish between filesystem space and “branch” space; branches and tags are ordinary directories within the filesystem. This is probably the single biggest mental hurdle that a CVS user will need to cross. Read all about it in Chapter 4, Branching and Merging.
Since Subversion treats branches and tags as ordinary directories, your project's various lines of development probably live in subdirectories of the main project directory. So remember to check out using the URL of the subdirectory that contains the particular line of development you want, not the project's root URL. If you make the mistake of checking out the root of the project, you may very well wind up with a working copy that contains a complete copy of your project's content for each and every one of its branches and tags. 
 That is, providing you don't run out of disk space before your checkout finishes.