Which one of Newton's Laws explains the motion of an object that is traveling with uniform circular motion?

A uniform circular motion is an example of accelerated motion.

When an object is moving in a uniform circular motion, there is a centripetal force acting towards the centre of the circular path and then a centrifugal force is also acting away from the centre of the circular path. The magnitude of the centripetal force and the centrifugal force is same but the direction is opposite to each other. So, it is explained by the Newton's third law.