If you do not know what glibc is by now, don't worry! When I first had problems with a new program I wanted to compile, I only knew that my version of glibc was not sufficient for the compile. Now that I know more, I will try to explain in a very simple way what glibc does.
The glibc package contains a library written in the programming language of C. Libraries are a very useful thing in programming; instead of inventing the wheel from scratch for operations such as computing the square-root of a number, such common functions are stored in separate files—the so-called libraries. When a new version of a library is published it often contains some new functions, uses more efficient algorithms for already implemented functions, and so on.
This is the reason why some programs complain about an older version of glibc: the current version just does not contain all the functions the program needs in order to run.
I know this is not technically correct in all detail, but it gives you a basic understanding of the architecture behind.