Wingtips prevent the large downwash (created by the vortices induced at the wingtips) immediately behind the wings from forming thus keeping a low effective angle of attack.
They might not prove beneficial on the 777 because although they reduce induced drag, they increase parasite drag. It might not be worth it.
I don't understand why boeing would introduce winglets on a very long haul 777. Induced drag decreases with speed and in cruise, the aeroplane is moving at it's quickest. Go figure
