UNIX systems have virtual memory. This means you can run a set of programs which occupy more space than the primary memory size of the computer.
Areas of memory not currently in use are swapped out onto disk. When a program needs to access something which is swapped out, it gets swapped in again and something else gets swapped out instead. In principle, this means that you can run arbitrarily large programs if you have enough disk. (In practice, programs very much larger than the primary memory size - 32MB to 64MB - run appallingly slowly.)
The amount of swap space available to each workstation is limited (a little larger than the primary memory size). If you have lots of things going on at once, it's possible to run out. For instance, each window on your screen has a running program behind it, using quite a lot of memory. If you get a message from the machine along the lines of "out of memory", it means you have run out of swap space, rather than exceeding your filestore quota.
Virtual memory was invented at the University of Manchester, on a machine called the Atlas, which was one of the fastest machines in the world in the early 1960s.