OK, imagine an large circular piece of aluminium with a hole in the middle of it, with a rod going through this hole (like in car wheels or dumbells) such that the aluminium disc is free to rotate around the rod.
Now imagine a horseshoe magnet placed so that the edge of the aluminium disc is between the north and south poles of the magnet. If you were now to move this magnet around the circumference of the disc, there would be relative motion between the magnetic field and the metal, and as you would know, eddy currents would be generated in this metal disc.
Due to these eddy currents, Lenz law kicks in and there is a force created that opposes you from moving the magnet relative to the disc. Now this force won't make it any harder to move the magnet at all, however it will make it harder to move the magnet RELATIVE TO THE DISC. This means that as the magnet is moved, the disc rotates around too with it (the resistance force caused by Lenz law opposes RELATIVE motion between the magnet and disc, not ABSOLUTE motion of the magnet). So as we move the horseshoe magnet around the circumference of the disc, we will see the disc moving too with the magnet.
Now imagine that we replace this horseshoe magnet with several electromagnets that are placed equal distances apart on the circumference of the disc. If we were to momentarily pass a pulse of current through each electromagnet sequentially (one after the other) in order, this would simulate moving a magnet around the disc (the magnetic field made by each electromagnet would "move" as one is switched off and the next is switched on). This would cause the aluminium disc to spin just like before with the horseshoe magnet. Note that the disc doesn't have to be made out of aluminium but any metal such as steel would do.
The benefits of the induction motors are that they're simple & cheap to manufacture, and more importantly have no wearing parts (no parts come into ontact with eachother) so there's less friction (making it more energy efficient and last longer).
Induction motors are a bit compilcated to understand, but just read this a couple of times and also read your textbook too and you'll understand how it works. HTH