A cap kit is the popular term used for the act of replacing old electrolytic capacitors on a monitor or television. The term also refers to the actual set of capacitors that you purchase to replace the old ones.
Electrolytic capacitors dry out over time, and begin to function poorly, or not at all. This is the reason why most televisions and monitors tend to start having problems at about ten years of age. That is when the caps start drying out.
The majority of picture problems in anything with a picture tube can usually be fixed with a cap kit. The basic idea is simple, you just unsolder the old caps, and solder on the new ones. It isn't a very difficult process at all. The only thing difficult about it is discharging the picture tube (which also isn't difficult, but can be scary).
Cap kits are most often done on arcade monitors. Simply because new ones are pretty expensive, and they are fairly easy to work on because the PCB boards are designed to be removed. You can order preassembled cap kits for most arcade monitors from several different vendors.
Televisions and computer monitors don't normally have preassembled kits available. So what you have to do is make a list of all the capacitors, and then take that to the electronics component place and get them individually (this is also what you do when you have an unidentified arcade monitor).
Computer monitors can be a real pain. Mostly because they often are not designed to have their cases opened up. I wouldn't even suggest trying to work on 15" monitors, as you can usually get good ones at the thrift store for a few dollars more than the caps would cost you.
When doing cap kits always look carefully at the old capacitors to make sure that the new ones go in the same way, as they have a positive and a negative side. The PCB is usually marked as to what is positive and what is negative, but it can be wrong. Use the original caps as your guide.