Imagine a circular track, about six feet in diameter (just short of two meters). Take a sort of pie-slice shape of that, place it on top of the track with wheels underneath, and give it a central pivot point, so the pie slice can rotate on top of the circular track. Then attach a riding car onto the wide end of the pie-slice. The car is shaped sort of like a quarter of an egg, the bottom half missing because of the floor and the other quarter missing to allow an entrance point. The pivot point is also at this entrance point, so you have to be careful to not trip over the large bolt while entering the car. The seat of the car faces the pivot point, so once spinning starts you are pressed back against the inside of the car, due to centrifugal forces. The seat is set into the egg-shape to provide just enough of a side wall to hold passengers inside while being pressed against it. About seven of these circular tracks with tilt-a-whirl cars are set on a platform that also moves in a circle. The platform has peaks and valleys, to help (or sometimes hinder) the momentum of the car spinning on its pivot point.

The car itself is like a miniature version of the earth, spinning on its axis. The platform would be like the orbit of the earth around the sun, only with peaks and valleys.

      ______/_                        \
     /       /\                        \
    /       /  \                        \
   /       /   |   <car           track> \
   |       |   |                          \
   |       |   |                           \
   |       |   |                           |
   |       |___|  <bench                   |  
   |       |   |                           |
   |        \   \_                         |
   |_________\____\_                       |
   \                                       /             
    \                                     /

Ok, so it's really tough to draw a pie-slice! I'm sure you get the idea. Seven of these tracks set in a circle on a platform with peaks and valleys. It's really quite an interesting ride, if you haven't been on one I highly recommend it.