There are generally two wattage numbers associated with sound equipment: Peak, and RMS. RMS is the maximum power rating in constant use, where Peak is just for short bursts... As such, the Peak rating will almost always be greater than the RMS rating.
When it comes to amplifiers (including the one built into most head units), the wattage rating is basicly a measurement of how forcefully it can drive a set of speakers.
When it comes to speakers, the wattage rating is a measurement of how forcefully the speaker can be driven before it burns out. The more wattage you feed a speaker the louder it will get, though actual sound volume you get per watt will depend on the speaker's specs (dB of sensitivity if I'm not mistaken... higher number = more sound per watt).
You can run a speaker rated at 50 watts RMS with an amp rated at 100 watts RMS, but if you turn the amplifier up too loud, you will be able to burn out the speaker (generally in the form of overheating and melting the voice coil former).
It's possible to burn out an amp too, but that generally only happens if you crank them up and run them with too low a load (ohms of impedance... you probably won't have problems if you stick with typical aftermarket head unit/speaker combinations), or with inadequate cooling.