As we know, The formula for calculaing the acceration of a uniform circular motion is a = (v^2) /r . This acceleration has a special name called centripetal accerleration. Newton told us that the force needed to produce accerleration equals the mass of the object times the accerleration of the object, so we got F = m*a = m * (v^2) /r = (m*v^2) /r 

The force in a uniform circular motion has a direction that points toward the center, and so people give it a name called centripetal force. The word "centripetal" means pointing to the center. The direction of velocity is perpendicular to the centripetal accerleration, and without the effect of centripetal acceleration, things are going to travel at the direction of its last velocity. Here is a good example:

Stand in the rain with your umbrella. When the rain drops accumulate on your umbrealla, rotate it hard. What you can see? By common sense, you are going to see the rain drops travelling perpendicular to the edges of the umbrella. When you rotate the umbrella, since nothing is acting as a centripetal force that pulls the rain drops towards the center, the rain can't keep on moving in centripetal motion and instead they move perpendicularly to the edges of the umbrella because of inertia when no centripetal accerleration exists.