I'm new to version control (currently using SVN), but I don't understand how this helps developers. What does version control do that makes it useful in a development environment?
VisualSVN and TortoiseSVN are just UI clients for SVN server. SVN server is source / version control system. Version control system is key asset for any real development because it stores versions of you your source codes. When using version control system you keep only local copy of source codes. The main copy is stored on version control system and you commits changes to the system.
VisualSVN is extension to Visual Studio which enables you using SVN repository directly from Visual Studio UI. TortoiseSVN is extension to Windows Explorer which enables you using SVN repository directly as you browse folders and files.
Version control offers a number of things:
Its a minimum for any software development work beyond just tinkering to see what happens.
I always warn anybody who is working with a version control system for the first time that avoiding it is only inviting trouble. They WILL run into a problem that when they look back they WILL realize it would not have happened if they used the system.