In the aircraft, you have AC breakers and DC breakers. Your DC breakers are generaly thermal, while your AC breakers are magnetic. In both cases, the circuit is opened by the breaker tripping which means that it has released itself mechanically. Overriding the mechanical holding device, regardless of whether it's thermal or magnetic, will restore power to the circuit if the circuit is still intact. Whatever short or overload condition caused the breaker to pop will be restored when you hold in the breaker. By pushing and releaing it, you're closing and opening a set of contacts...just like points in a magneto, and inducing a voltage spike and evn possibly a spark somewhere.
The circuit breaker is not intended to protect the load bearing device on the circuit. If you have a pump, for example, with a circuit breaker for that circuit...the CB isn't there to protect the pump. The circuit breaker is there to protect the wiring. If something burns up or melts, that's where it's going to happen in most cases, and it's the wiring that's being protected. Ultimately it's you being protected.
Using circuit breakers as switches is a bad idea; it's a poor practice that causes arcing and wears out the breaker. A magnetic breaker is nothing more than a small electromagnet that opens the circuit via a solenoid. Electrically the circuit is opened by causing enough of a force on the solenoic (the breaker itself) that it overcomes mechanical resistance, usually from a little piece of plastic. Every time you pull that breaker, you casue wear and stress on that plastic, and will eventually change the value at which the breaker opens...eventually it will ultimately not stay closed. You'll also be promoting electrical wear and arcing in the breaker.
A thermal breaker uses dissimiliar metals and the heating properties thereof to open the breaker. A little bimetalis strip releases the breaker when it's heated. By knowing the physical properties of the strip, size, etc, the manufacturer can set it to open withinin a given tolerance of resistance...when it heats up to a given value under a given load and flexes, it opens the circuit breaker. Holding it closed is doing nothing more than restoring the circuit forcefully.
A short which has caused a circuit breaker to open is a problem. Restoring power to that circuit isn't helping anything. You may cause a fire, or cause damage to the components served by that circuit. Or, what caused the breaker to pop may be something entirely different. Shorts from one wire to another, or one component to another, may mean that the breaker that just blew or popped isn't the problem at all. Something to definitely keep in mind.
Trip free circuit breakers are used in aircraft, but don't make the assumption regarding what's in your panel. CB's are often mixed. Essential breakers are often resettable, which means you can certainly restore power by holding it it and thereby do damage. Respect the circuit breaker; it's doing an important job that's only in your best interest.