I'll try to shed some light on different flap systems and what they are good for.
As Cedarjet already mentioned, slats and flaps are "high lift devices". The lift provided by a wing follows Bernoulli's law:
A = rho/2 * v² * ca* S
in this formula A is the lift provided, rho is the density of the air, v is the speed of the airflow around the wing, ca is the lift coefficient (dependent on the actual profile and the angle of attack) and S is the wing area.
Having a look at the formula it becomes clear that the lift provided by the wing is the bigger the faster the aircraft travels and the bigger the wing surface F is.
Given the situation on takeoff, the plane should actually climb (at least, that's what it is supposed to do, right?), therefore the force of the lift must be bigger than the gravity force.
So, coming back to the topic: To increase lift in such a situation (where the speed is rather low (as it is on landing), you could
a) increase the lift coefficient
b) increase wing area
That's exactly what flaps are supposed to do.
There are different flap systems:
plain flaps: almost looking like rudder surfaces and often found on smaller aircraft. They do not enlarge the wing surface, but increase the curvature of the wing, and therefore the lift coefficient ca.
split flaps: they only affect the lower side of the wing, whereas the upper side remains untouched. They are a little more efficient than plain flaps, as a small part of the airflow from under the wing is directed through a gap to the upper side of the wing surface. so it reduces the danger of a stall. On the other hand, this system produces more drag than the plain flaps
fowler flaps (as a special form of slotted flaps): Fowler flaps do both, they increase the curvature of the wing and therefore the lift coefficient ca, but they also increase the wing area, they are slotted for the same reason as there is a gap in the splitted flaps:to let some air flow from the lower to the upper side of the wing and therefore to reduce the danger of a stall of the airflow on the upper side.
Problem is, as you mentioned, that these forms of flaps are very complicated. The reason they are used is simple. Big aircrafts need very much lift for takeoff and landing (regarding that the takeoff/landing speed of a B747 is not THAT different of the speeds of a much smaller B737). Therefore, often bigger aircraft have much more complex flap/slat systems.
Hope that Helps
[Edited 2005-03-27 20:49:15]