Linux supports virtual memory, that is, using a disk as an extension of RAM so that the effective size of usable memory grows correspondingly. The kernel will write the contents of a currently unused block of memory to the hard disk so that the memory can be used for another purpose. When the original contents are needed again, they are read back into memory. This is all made completely transparent to the user; programs running under Linux only see the larger amount of memory available and don't notice that parts of them reside on the disk from time to time. Of course, reading and writing the hard disk is slower (on the order of a thousand times slower) than using real memory, so the programs don't run as fast. The part of the hard disk that is used as virtual memory is called the swap space.
Linux can use either a normal file in the filesystem or a separate partition for swap space. A swap partition is faster, but it is easier to change the size of a swap file (there's no need to repartition the whole hard disk, and possibly install everything from scratch). When you know how much swap space you need, you should go for a swap partition, but if you are uncertain, you can use a swap file first, use the system for a while so that you can get a feel for how much swap you need, and then make a swap partition when you're confident about its size.
You should also know that Linux allows one to use several swap partitions and/or swap files at the same time. This means that if you only occasionally need an unusual amount of swap space, you can set up an extra swap file at such times, instead of keeping the whole amount allocated all the time.
A note on operating system terminology: computer science usually distinguishes between swapping (writing the whole process out to swap space) and paging (writing only fixed size parts, usually a few kilobytes, at a time). Paging is usually more efficient, and that's what Linux does, but traditional Linux terminology talks about swapping anyway.
When you're looking at the top output, you should see three parameters for virtual memory.
VIRT stands for the virtual size of a process, which is the sum of memory it is actually using, memory it has mapped into itself (for instance the video card’s RAM for the X server), files on disk that have been mapped into it (most notably shared libraries), and memory shared with other processes. VIRT represents how much memory the program is able to access at the present moment.
RES stands for the resident size, which is an accurate representation of how much actual physical memory a process is consuming. (This also corresponds directly to the %MEM column.) This will virtually always be less than the VIRT size, since most programs depend on the C library.
SHR indicates how much of the VIRT size is actually sharable (memory or libraries). In the case of libraries, it does not necessarily mean that the entire library is resident. For example, if a program only uses a few functions in a library, the whole library is mapped and will be counted in VIRT and SHR, but only the parts of the library file containing the functions being used will actually be loaded in and be counted under RES.