The term Hop-up, short for High Operation Power Up, describes the back-spin put on airsoft pellets and BB's to increase their range and (vertical) accuracy via Magnus effect. Hop-up acts somewhat like the rifling on the barrel of a firearm, but without the increase in horizontal accuracy. Also, being light-weight, airsoft pellets are still affected by wind when fired.
Airsoft hop-up devices apply a backspin to the pellet so that the pressure force acts on the pellet opposite to the direction that gravity is pulling it. This causes the pellet to fall less over a given distance than it would without the spin applied to it.
In airsoft guns this is often implemented as a rubber piece at the rear of the barrel that is thicker at the top of the barrel than the bottom. As the pellet moves past this piece it tends to roll, inducing a backspin. This is most often adjustable so that the effect can be tuned to suit the weight or speed of the pellet and each player's preference.
The primary cause of the apparent lift on an airsoft pellet is the Magnus effect. There is a layer of non-moving air on the surface of the pellet (boundary layer). This is why a golf ball has dimples; this layer acts like ball bearings. In the case of a spinning ball, this layer gets thrown off at an angle. Newton's laws say that in order for air to be thrown in one direction, the ball has to move in the other direction. According to the Magnus explanation, the rotating ball would throw air downward and to the rear, thus giving lift. The air on the bottom of the ball is slowed down, so when the separated air comes back together, it is lower than the middle of the ball, appearing like a comet's tail pointing down. This can be verified in wind tunnels and is very well documented in fluid dynamics textbooks.