There are two reasons to move slowly. The first is raising awareness: For instance, how do you walk?  Dou you walk heavy footed (stomping) or light? (like a cat) Do you roll heel to toe or do you place the entire foot flat on the floor? In Tai Chi, you will step slowly, lightly and very deliberately. By slowing down the process of walking, you become aware of your balance or your lack of balance through the entire movement. If you are doing something like stepping too far, leaning too far, or putting weight into a foot before you are sure of what's under it, you become aware of it immediately. 

The other reason for moving slowly is to build strength. When you begin Tai Chi, you will begin with a simple posture called Wu Chi. In this stance you will bend your knees and sink your weight, putting all the work back on your glutes, your abdominal muscles and thighs. Throughout the form, your power is primarily derived through the legs. Doing the movements of tai chi slowly keeps your muscles engaged at all times.