Centrifugal force occurs when inertia acts upon an object. As in the case of whirling a bucket of water on a string:

Bucket at rest:
\=============/
|=============|
|=============|
|=============|
|=============|
|=============|
|~~~~~~~~~~~~~|
|=============|
\_____________/

(Down is here)
(So is gravity)

Bucket starts moving:

\=============/
|=============|
|============~|
|=========~=~=|
|======~=~====|
|===~=~=======|
|~=~==========|
|=============|
\_____________/
(Down is over here now)
(Same with gravity)

Bucket attains full speed:

\=============/
|=============|
|=============|
|=============|
|=============|(Gravity)
|=============|
|~~~~~~~~~~~~~|
|=============|
\_____________/
(Down)

Centrifugal force relies a great deal upon one's point of view. To the spectator inside the bucket, there's a slight difference in weight, accompanied with some nausea by seeing everything outside the bucket twirling wildly.

However, to the person rotating the bucket, the water 'sticks' to the inside of the bucket, refusing to fall out.

The phenomenon relates, as I stated earlier, to inertia.
Take, for example, a car rounding a curve, and you're pushed against the wall. This happens because you and the car are seperate objects, both affected by inertia. Initally, both you and the car are moving in a straight-line path. As the car turns, you continue to move in a straight line, as per Newton's First Law.
This straight-line motion pushes you into the wall of the car, while the car is turning, producing what we call centrifugal force.