Bouldering is the act of low climbing, without the use of ropes and harnesses. It can be done on your own and does not require any prior instruction. The use of a spotter is highly recommended.
Top Roping is where the rope is already set up on the wall for you. The climber and belayer attach to opposite ends of the rope, and the climber ascends the wall, while the partner pulls up slack in the rope through a belay device.
Lead Climbing is a more advanced form of climbing and one that is commonly seen when climbing outside. In lead climbing, the climber brings their rope up the wall with them as they climb, clipping into the carabiners attached to the wall. Lead climbing requires advanced training, and a well-developed climbing ability (5.9 or above) to be comfortable leading.