In particular, the number of 'poles' describes the shape of the magnetic field produced inside the motor.
In a conventional induction motor, magnetic flux threads across the 'airgap', the space between the rotor and the stator. Just like a conventional bar magnet, some parts of the stator will be north poles, and some parts will be south poles. In operation, the position of the poles rotates.
The magnetic field will rotate by one pair of poles per AC cycle. So when you feed 60Hz AC into a 2 pole motor, the magnetic field will rotate 60 times per second, or 3600 RPM. If you feed 60Hz AC into a 4 pole motor, the magnetic field only rotates half a turn per AC cycle, or 30 times per second, or 1800 RPM