When an object moves in a circular path it accelerates towards the center of the circle as a result of what?

 Here, first it is needed to understand definitions of the velocity and acceleration.

Velocity is the change in displacement per unit time. And acceleration is the change in velocity per unit time. It is noted that displacement is a vector quantity, thus, ultimately velocity and acceleration are also vector quantities. 

It means velocity can be changed with time by magnitude or direction. While a substance is rotating about any center with velocity 'v' which magnitude is uniform. But due to rotational motion, the direction of the velocity is changing continuously. This cause the acceleration which is radially . And this know as centrifugal acceleration. When substance is tied by string to the centre, then there is a reaction force is produced to oppose the centrifugal force, which is known as centripetal force. This centripetal force causes the centripetal acceleration which is radially inward.