Acceleration is the rate of change in velocity. Velocity is basically speed, but in a certain direction. So, as an object goes in a circle, it is constantly changing direction, right? You could say it is changing velocities. So, because acceleration is the rate of change in velocity, it is accelerating, even though it might be going at a constant speed.
Please comment, if this doesn't make sense. I can explain it further if you still don't get it.