Pinch flats usually happen when you hit a sharp rock or ledge and your tire pressure is a little on the low side. When the pressure in the tire is too low to prevent the rock or ledge from compressing the tire all of the way up to the hard rim, your tube is literally left between a rock and a hard place.
Pinch flats usually result in double punctures about an inch apart in your tube. This is commonly known as a snake bite. It happens because the the contact usually occurs on both sides of your rim.