In this movie, you see a simulation of an object moving in a circular path. Notice that the velocity vector (in blue) is constantly changing direction. Even though the magnitude (amount) of the velocity stays constant, the direction is changing. This shows that the object is accelerating. Remember that acceleration is defined as the rate of change of velocity. So any change, even if it is just the direction, is an acceleration. Another way to think about this is to consider that to change your direction of motion requires a net force, and a net force causes acceleration. 

It is important to notice that the velocity vector of this object is always tangent to the circular path it is traveling.

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