I've noticed that the wings on the A380 are very curved in comparison to the 747. I mean the 747 has a lot of wing flex but the A380 has less wing flex and the wings are flexed down in comparison to the 747. Here there are two photos that might help you understand what I'm writing. So why are the A380 wings like that and what are the benefits? Source
The wings are designed like that. You can see them in the picture below.
Image from airliners.net
The A380 wings are designed to be the most efficient while still inside the 80m 'box' for efficient airport operations. The result is a clean slate design which used CFD extensively to get the most efficient aerodynamic design possible.
The 'curve' near the root means that the landing gear in the wings could be as short as possible while being long enough to prevent a tail strike during rotation and allowing the spar to pass below the floor.
The shape also allows enough ground clearance for the inboard engines. This assumes importance with the advent of engines with ever higher bypass ratios.
Of course, the use of modern composite materials means the the wing 'flexes' up to be more or less straight once the aircraft is airborne.
(wikimedia.org) In-flight 'flex'.
Aeroalias answer already covers most points. Still it may be worth to add that its not a clear gull wing, but more toward a dihedral setup with an increased volume at the front root part. This is most obvious when looking at it from the back while flying.
There are not many pictures showing one flying and from behind but this (taken from Wikipedia) might give a hint:
Beside the already mentioned advantage of shorter and thus lighter landing gear and more room for engine mount (much like the Ju87 inverted gull wind gid provide),
a dihedral wing also increases lateral stability in flight.
Increased comfort was as well one of the ambitious design criteria for the A380. Who ever had the chance to board one did enjoy the results. So considering the many, often each other contradicting requirements for wing (and fuselage) design, this marks a sweet spot - at least when reaching a certain size :))