Monitoring your circuit breakers can be a good way to keep tabs on your home's electrical system, allowing you to ensure that everything's working properly. If a circuit breaker becomes hot to the touch, however, this can be a sign of a serious problem.
Current and Resistance
The natural resistance in copper wiring means that any current passed through it will produce heat as a byproduct. It's natural for wiring to become warm while in use.
If a breaker becomes hot to the touch, however, it can be a sign that the circuit is overloaded. Take a look at what's connected to that circuit, and move high-drain appliances somewhere else.
Another reason a breaker might become hot is if it was improperly installed. Circuit breakers are designed to automatically trip when the current reaches a certain level; if the installed breaker is the wrong type, it can allow too much current through for the wiring to handle safely.
A short circuit caused by a defective breaker can also cause the system to overheat. In this case, the switch will need to be replaced.
An overheated breaker should be shut off until you can identify the source of the problem.