A case lamp (also called a Case Light) is quite simply, a lamp which one places inside their computer. This is a common practice among case modders.
Now, one problem one would think that this has, is that a lamp would heat up your case, and since
Overclock + Heat = Bad
this is not a good prospect.
Have no fear, however! Case lamps are not your run-of-the-mill light bulbs. Case lamps are Cold-cathode flourescent lamps. In other words, they don't make heat, or make so little that the amount is negligible, even to an overclocker, and that says something, since the CPU is a fragile and delicate piece of equipment.
One would also think that, "Hey, what's the point of a lamp if you can't see inside your computer?" Well, the thing is, using case lamps ties in the overclocker subculture, which ties in with the LAN Party, which ties in with showing off your box, which ties in with case modding. A modder will either cut a hole in the side of their box and cover it with plexiglas or lexan, or buy a pre-made transparent case or a case with a window built in. One way or another, the case becomes translucent.
There are two purposes to a case lamp. One, it allows people too see your hardware.
Hey man, you better take that box back to the circus before they find out it's gone!
With a lamp, they see your GeForce 4 and your SB Live! Audigy Platinum. They see your 1.2 Gigabytes of RAM. And when you go to LAN Parties with your box, people see it. It can be intimidating. Really, it can!
The other reason would be simply that the effect looks insanely cool.
This also goes well with spray-painting your box black, and giving it a name.
Sources: thermaltake.com, friends, personal experience