human biology - What actually happens when my leg 'falls asleep'?

The explanation in the link Polynomial posted is essentially correct.

Whenever there is a reduced or blocked blood supply (ischaemia) to your extremities, the 'five P's' can occur: pulselessness, pain, pallor (colour), paresthesia (numbness) and paralysis (or weakness).(1).

The numbness and weakness happen after the blood flow have been reduced for a particularly prolonged period.

Cells in our body require a blood supply to stay alive (think about a stroke or heart attack for example). So a reduced supply can cause them to function abnormally or after a time (depending on the cell or tissue type) die.

So with a 'sleeping leg', staying in an awkward or particular position where arterial blood supply is blocked or reduced to the leg, the muscle, nerve tissue etc all lack supply hence causing sensory disturbance and weakness.

The possible buildup of metabolites could also contribute to the symptoms (pain).

Hope that helps!

1. Miller's Anaesthesia - Miller.