In the case where the curved path produced by this force perpendicular to the direction of motion is a circle, the resulting acceleration is directed along the radius of the circular path. This "center seeking" acceleration is called centripetal accleration and the force which produced that acceleration is called a centripetal force.
Centrifugal force is sometimes called a fictitious force because it is only a manifestation of the tendency of things to travel in straight lines when no force is applied to them. Imagine you are riding in a car with very slippery seat covers. The car is travelling in a straight line initially and then the driver starts a gentle turn to the left. Because the car now has some centripetal acceleration but you do not, due to the almost frictionless seat covers, the car turns left but you continue in a straight line. It will seem to you that there is a force pushing you toward the right end of the seat. That is the centrifugal "force". When you come into contact with the car door at the right end of the seat, it will apply a force to you, giving you a centripetal acceleration, causing you to take the same path as the car.