In a typical system, a number of programs will be running. Each program relies on a number of functions, some of which will be "standard" C library functions, like printf(), malloc(), write(), etc.
If every program uses the standard C library, it follows that each program would normally have a unique copy of this particular library present within it. Unfortunately, this results in wasted resources. Since the C library is common, it makes more sense to have each program reference the common instance of that library, instead of having each program contain a copy of the library. This approach yields several advantages, not the least of which is the savings in terms of total system memory required.