In physics, uniform circular motion is rotation along a circle at constant speed.When an object moves in a circle at the same speed, we can't see it travels at the same velocity. That is because even if the object moves at same speed, the direction changes all the time. And since the direction changes make the velocity (velocity is a vector, not a scalar, so it has directions) different all the time, we will same the object is always accelerating.
In uniform circular motion, the direction of acceleration is pointing inwards, towards the center, while the direction of velocity is perpendicular to the direction of acceration. You can understand better if you look at the picture below:
But why? Try this if you still don't understand: Find a place no one is around. Tie your door key to a string and then hold the end without the key attached and whirl it over your head. (Be careful and make sure no one is around before you proceed!! Seriously) Suddenly you release the string. As you will see, the key and the string doesn't go in a circle after you release it. Its moving direction is perpendicular to accereration! That is the direction of the velocity at the moment you release it!