Question: Forgive me, but I don't know the technical term to know what to search for.

I am trying to find a way to keep track of changes in my code during the development of my program. something that would allow me to go back to a section of code that I deleted. I am not talking about "undo". But rather a way that would let me keep track or be able to retrieve a section of my code that I deleted but now want it back.

Is there such a way? If there is, then what is this whole system/procedure called? Is there something that integrates with Visual Studio 2010?

Answer: 
you could use 

**SVN**
or
**GIT**

but for local use, I would prefer SVN. its free and its easy.
For visual studio there are a few SVN client plugins (like VisualSVN). But, I would suggest TortoiseSVN as the client.

To be clear, SVN is the server, TortoiseSVN is the client. (Both are free open source tools)
subversion has a lot of mind share these days, but it's very old-school, first-gen tech. Distributed revision control is gaining a lot of momentum and I'd highly recommend that you become familiar with it if you're going to be a code monkey professional. Look up mercurial (also referred to as hg) or bazaar. If nothing else, perforce - a professional, commercial revision control tool - is free for up to two users. It works very well, as long as you keep your branching craziness to a minimum.