Condenser mics work via an element that has charged plates -- an electrical device called a capacitor or a condenser (hence the name). The power to charge the plates needs to be supplied in some fashion. Phantom power is the most common means, a way that allows the power to be supplied via the XLR mic cable.
A preamp is an amplifying circuit that raises the very tiny signal produced by a microphone's transducer to line level so it can be recorded. All mics require a preamp. Only condenser mics require phantom power too. Most mic preamps also provide phantom power.
As far as damaging a mic, I believe it might not be a good idea to plug a condenser in with the phantom power already applied. I think some condenser mics might use different voltages than the most common 48 V and it might damage the element to use the wrong power source. Other than that, I'm not sure how else they might damage a mic. I'm pretty sure a dynamic mic would not be damaged by having phantom power on.