Reading from a disk is very slow compared to accessing (real) memory. In addition, it is common to read the same part of a disk several times during relatively short periods of time. For example, one might first read an e-mail message, then read the letter into an editor when replying to it, then make the mail program read it again when copying it to a folder. Or, consider how often the command ls might be run on a system with many users. By reading the information from disk only once and then keeping it in memory until no longer needed, one can speed up all but the first read. This is called disk buffering, and the memory used for the purpose is called the buffer cache.
Since memory is, unfortunately, a finite, nay, scarce resource, the buffer cache usually cannot be big enough (it can't hold all the data one ever wants to use). When the cache fills up, the data that has been unused for the longest time is discarded and the memory thus freed is used for the new data.
Disk buffering works for writes as well. On the one hand, data that is written is often soon read again (e.g., a source code file is saved to a file, then read by the compiler), so putting data that is written in the cache is a good idea. On the other hand, by only putting the data into the cache, not writing it to disk at once, the program that writes runs quicker. The writes can then be done in the background, without slowing down the other programs.
Most operating systems have buffer caches (although they might be called something else), but not all of them work according to the above principles. Some are write-through: the data is written to disk at once (it is kept in the cache as well, of course). The cache is called write-back if the writes are done at a later time. Write-back is more efficient than write-through, but also a bit more prone to errors: if the machine crashes, or the power is cut at a bad moment, or the floppy is removed from the disk drive before the data in the cache waiting to be written gets written, the changes in the cache are usually lost. This might even mean that the filesystem (if there is one) is not in full working order, perhaps because the unwritten data held important changes to the bookkeeping information.
Because of this, you should never turn off the power without using a proper shutdown procedure or remove a floppy from the disk drive until it has been unmounted (if it was mounted) or after whatever program is using it has signaled that it is finished and the floppy drive light doesn't shine anymore. The sync command flushes the buffer, i.e., forces all unwritten data to be written to disk, and can be used when one wants to be sure that everything is safely written. In traditional UNIX systems, there is a program called update running in the background which does a sync every 30 seconds, so it is usually not necessary to use sync. Linux has an additional daemon, bdflush, which does a more imperfect sync more frequently to avoid the sudden freeze due to heavy disk I/O that sync sometimes causes.
Under Linux, bdflush is started by update. There is usually no reason to worry about it, but if bdflush happens to die for some reason, the kernel will warn about this, and you should start it by hand (/sbin/update).
The cache does not actually buffer files, but blocks, which are the smallest units of disk I/O (under Linux, they are usually 1 KB). This way, also directories, super blocks, other filesystem bookkeeping data, and non-filesystem disks are cached.
The effectiveness of a cache is primarily decided by its size. A small cache is next to useless: it will hold so little data that all cached data is flushed from the cache before it is reused. The critical size depends on how much data is read and written, and how often the same data is accessed. The only way to know is to experiment.
If the cache is of a fixed size, it is not very good to have it too big, either, because that might make the free memory too small and cause swapping (which is also slow). To make the most efficient use of real memory, Linux automatically uses all free RAM for buffer cache, but also automatically makes the cache smaller when programs need more memory.
Under Linux, you do not need to do anything to make use of the cache, it happens completely automatically. Except for following the proper procedures for shutdown and removing floppies, you do not need to worry about it.