Rim brakes squeeze the wheel's rim directly with a pad; disc brakes squeeze a separate rotor mounted at the wheel's hub. Both are safe, well-proven systems — the choice comes down to where and how you ride.
Disc brakes perform more consistently in wet weather, since the rotor sits away from road spray that coats a rim. They also don't wear down the rim itself over years of use. The trade-off is a bit more weight and a slightly more involved (though still routine) maintenance process.
Rim brakes are lighter, simpler to service at home, and generally cheaper to maintain — pads are inexpensive and easy to swap. For flat, mostly-dry commuting, rim brakes are still a perfectly sound choice; for hilly terrain or frequent wet-weather riding, discs earn their extra weight.