"Source control" refers to the concept of storing all files that make up the source of an application in an (usually online) repository - where one can manage with fine detail exactly what has changed in the source code between versions, manage issues, involve other people with the project, and generally provide a platform to collaboratively manage a project.
The term is usually synonymous with version control - although you can have a repository and not explicitly name versions. Version control in particular just refers to labeling major versions of your project with a hierarchical numbering scheme (1.2.4 etc.)
There are several different tools that implement different kinds of source control. For example, Git is a source control tool that sets lets you manage a project. Github is a web-site that repositories managed with Git are usually stored on. Mercurial is yet another source control tool.
Typically, source control can be complicated to understand, and usually requires significant time studying tutorials. A lot of concepts are unfamiliar to solo programmers who have only worked on small projects. Changes to source code are managed through commits, and different branches of the project can be worked on by multiple people. Changes from separate branches can be merged, and the project can be forked by another user entirely (at least for Git).
Making your library open source is a good idea, and it's not too hard to give it a home on github. I would look into some resources to find out how to set it up.