Memory fragmentation is the same concept as disk fragmentation: it refers to space being wasted because the areas in use are not packed closely enough together.
Suppose for a simple toy example that you have ten bytes of memory:
| | | | | | | | | | |
0 1 2 3 4 5 6 7 8 9
Now let's allocate three three-byte blocks, name A, B, and C:
| A | A | A | B | B | B | C | C | C | |
0 1 2 3 4 5 6 7 8 9
Now deallocate block B:
| A | A | A | | | | C | C | C | |
0 1 2 3 4 5 6 7 8 9
Now what happens if we try to allocate a four-byte block D? Well, we have four bytes of memory free, but we don't have four contiguous bytes of memory free, so we can't allocate D! This is inefficient use of memory, because we should have been able to store D, but we were unable to. And we can't move C to make room, because very likely some variables in our program are pointing at C, and we can't automatically find and change all of these values.
How do you know it's a problem? Well, the biggest sign is that your program's virtual memory size is considerably larger than the amount of memory you're actually using. In a real-world example, you would have many more than ten bytes of memory, so D would just get allocated starting a byte 9, and bytes 3-5 would remain unused unless you later allocated something three bytes long or smaller.
In this example, 3 bytes is not a whole lot to waste, but consider a more pathological case where two allocations of a a couple of bytes are, for example, ten megabytes apart in memory, and you need to allocate a block of size 10 megabytes + 1 byte. You have to go ask the OS for over ten megabytes more virtual memory to do that, even though you're just one byte shy of having enough space already.
How do you prevent it? The worst cases tend to arise when you frequently create and destroy small objects, since that tends to produce a "swiss cheese" effect with many small objects separated by many small holes, making it impossible to allocate larger objects in those holes. When you know you're going to be doing this, an effective strategy is to pre-allocate a large block of memory as a pool for your small objects, and then manually manage the creation of the small objects within that block, rather than letting the default allocator handle it.
In general, the fewer allocations you do, the less likely memory is to get fragmented. However, STL deals with this rather effectively. If you have a string which is using the entirety of its current allocation and you append one character to it, it doesn't simply re-allocate to its current length plus one, it doubles its length. This is a variation on the "pool for frequent small allocations" strategy. The string is grabbing a large chunk of memory so that it can deal efficiently with repeated small increases in size without doing repeated small reallocations. All STL containers in fact do this sort of thing, so generally you won't need to worry too much about fragmentation caused by automatically-reallocating STL containers.
Although of course STL containers don't pool memory between each other, so if you're going to create many small containers (rather than a few containers that get resized frequently) you may have to concern yourself with preventing fragmentation in the same way you would for any frequently-created small objects, STL or not.