Why wear them?
Flight sox are recommended for anyone flying for over four hours as there is a well documented increase in DVT (deep vein thrombosis) on long haul flights. Flight socks significantly reduce the risk of DVT as they aid the return of venous blood from the lower legs to the heart.
The main problem with long haul flights is lack of movement of the foot and lower legs. We usually use 'muscle pumps' in these areas to pump blood back to the heart. When the muscles aren't being contracted blood pools in the lower legs and can stagnate to the point that the blood coagulates or clots causing either a 'superficial thrombophlebitis' (clot in the superficial veins) or a deep vein thrombosis (DVT is a clot in the deep veins).
As well as wearing flight socks you need to increase fluids to prevent dehydration, minimise alcohol and walk around as often as is practicable during long flights.
If you are older than 60, have a family or personal history of DVT, are overweight or smoke or have varicose veins then you are at increased risk of DVT and flight sox become even more important.