I'll give this a try.
The Coriolis effect is referred to as an "apparent force" because it actually isn't real, but appears to be real to an observer in an accelerating reference frame. It's actually a correction factor that has to be applied to a force equation, in order to work out the real forces acting on an object, where the observations of the behavoir of that object, are distorted by the accelerating reference frame.
Here's an example to illustrate.
Assume a merry-go-round, with a cup to receive a golf ball in the middle. Also, assume a grid of lines on the merry-go-round surface, layed out as a series of radius lines extending from the center outward to the edge, and a series of concentric circles with the cup as the center of the circles. Assume the grid lines will be used to measure the forces acting on a golf ball.
Also assume that a level platform is located right next to the edge of the merry-go-round, with a surface height equal to the height of the merry-go-round's surface. Assume also that there's a chair on the edge of the merry-go-round facing the cup, to allow an observer to watch the actions of a golf ball.
Now we putt a golf ball from the platform to the cup, with an observer sitting in the chair, while the merry-go-round is stationary. In this case the observer can easily see that the only force acting on the golf ball, was the linear force applied to the ball by the putter. No other force was apparent to the observer, as the golf ball moved in a straight line from the platform to the cup. The observer watched the motion of the golf ball, and used his grid measurement system that was NOT in accelerating motion, to observe the motion of the golf ball.
Now lets assume that the merry-go-round is put in motion at a constant rate of rotation. Rotation is an accelerating reference frame because all rotating objects are undergoing directional acceleration, even when the rate of rotation remains constant.
Now we again putt the golf ball from the platform to the cup, with an observer in the chair, and we'll assume that the surface of the merry-go-round is basically frictionless. Because the observer of the event is now in an accelerating frame of reference, the golf ball will appear to him to have mutliple forces acting on it. An "apparent force" will appear to the observer to cause the golf ball to move in an inwardly directed spiral towards the cup. The observer's accelerating reference frame has now distorted his observation, because both he and his grid measurement system are part of the accelerating reference frame.
So now the observer sees a "coriolis force" acting on the golf ball. The force is not real, but it's apparent to him. So from his vantage point, he has to apply the "coriolis force" as a correction factor to a force equation, in order to figure out what really happened to the golf ball, from his acceleration distorted viewpoint.
I hope this makes sense.