Can re-closing a circuit-breaker be dangerous?
When it first trips, you should first eliminate any causes for it to trip before resetting it.

A standard circuit breaker (not a GFCI or AFCI) will trip because too many amps are pulled. If this is powering outlets, then unplug everything on the circuit. If it still trips, then either you didn't notice the fork stuck in one of your outlets (I had an exciting childhood), the problem is with a hardwired appliance, or there's a short, and you should get an electrician out to diagnose.

If it doesn't trip with everything unplugged, then it could be an overloaded circuit, which would still require an electrician to run a new circuit. However, overloaded circuits often take a short time to trip, and it would more likely be a faulty device that you can detect by plugging things in one at a time until the breaker trips again. Note that if any wires or extension cords are worn or frayed, then they are a fire and electrocution hazard and should not be used.

If the breaker is a GFCI (typically seen with outdoor or bathroom/kitchen outlets), then in addition to triggering on amps, it can also trigger when current is going to a ground. You can try the same diagnosis as above, but realize that this is a significant risk of electrocution if you become a better ground than the path the current has already found.

If the breaker is an AFCI (typically seen in newer homes to bedroom outlets), then it can also be tripping because of a an arcing current, either from a short in the wiring, a frayed wire, etc. This is an immediate fire risk rather than the slightly slower fire risk you expose yourself to by overloading the wiring with too many amps.

In all cases, if you can't isolate it to a bad device that you can unplug, get an electrician out to diagnose and repair. The risk of fire or electrocution is too great.