Originally Posted by Red Herring

It's a starter motor issue. Basically starter motors have a small gear that moves out and engages with the flywheel when you want to start the engine, and it then disengages once the engine is running so that the starter doesn't keep spinning when not in use.

This gear can be moved out in one of two ways, pre-engaged or inertia type.

The pre-engaged one uses a solonoid to move it out and as the gear engages a circuit is completed and the starter motor starts to spin. These are the ones that go click sometimes and nothing happens until you give it a smack with a hammer....
This doesn't sound like yours as the motor is spinning without engaging with the flywheel.

On the inertia type the gear is mounted on a bendix (a spiral on the shaft) so when you turn the key the starter immediately starts to spin and in doing so it flicks the gear out and it engages with the flywheel. Sometimes (usually in cold weather when the grease is a bit think and sticky) the gear doesn't fly out properly so doesn't hook up with the flywheel (can also happen if the battery is a bit weak and doesn't get things moving fast enough) and then you get the scenario where the starter motor is spinning, but not turning over the engine.....like what you got! Quick fix is to stop (like you did) and then turn the key again hoping that second time round it flicks out (like it did).

Check your battery, if that's OK then you probably need to have the starter off and lubricate the bendix properly.