Theory:

Tie a piece of thread to a small stone at one of its ends. Rotate the stone in a circular path with constant speed by holding the thread at the other end.
 
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Rotating a stone
 
Now release the stone and observe in which direction does the stone travel.
 
When the stone is released, it moves in a straight line tangential to the circular path. This happens because when the stone is released, it continues to move along the same direction it has been moving at that instant. The object moves along a tangential line to show that the direction of motion of the stone changes at every point.
 
This clearly shows that the direction of motion of that stone is changed when moving along the circular path.
 
Therefore, we can state the uniform circular motions as,
If an object moves with constant speed in a circular path, then the motion is called uniform circular motion.
Illustration:
In a sporting event like hammer throw, the athlete holds the hammer in his or her hand, rotates the body in a circular motion, and then throws the hammer. The moment when the hammer is released, it goes in the same direction as it was going while releasing the hammer.
 
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Hammer throw
Example:
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Motion of the moon and the earth
 
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A satellite in a circular orbit around the earth
 
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A cyclist on a circular track moving at a constant speed
Reference:
https://www.stockvault.net/data/2016/07/12/204199/preview16.jpg