A routine or procedure P is reentrant (or pure code) if it can be “re-entered” after it is already in execution. Basically, it means that P can be executed two or more times simultaneously, or alternatively, that P can be safely executed concurrently. There are some conditions P must follow in order to be reentrant, and we may check them in the Wikipedia entry for reentrant functions.
Some programs necessarily have to be reentrant. For instance, device drivers. A device driver has to be reentrant because another interrupt may be raised while the driver is running. This means that reentrancy allows for code sharing. For example, if a program consists of 600 KB of code and 200 KB of data, and n users are simultaneously using the program, we would require n x 600 KB of physical memory for the code if the program is not reentrant. But if the code is reentrant we can share it among the n users, saving a lot of memory.