The Glibc package contains the GNU C Library.
The C Library is a collection of commonly used functions in programs. This way a programmer doesn't need to create his own functions for every single task. The most common things like writing a string to the screen are already present and at the disposal of the programmer.
The C library (actually almost every library) come in two flavors: dynamic ones and static ones. In short when a program uses a static C library, the code from the C library will be copied into the executable file. When a program uses a dynamic library, that executable will not contain the code from the C library, but instead a routine that loads the functions from the library at the time the program is run. This means a significant decrease in the file size of a program. The documentation that comes with the C Library describes this in more detail, as it is too complicated to explain here in one or two lines.