The upward component of force imparted onto objects moving through air.
Lift can be generated by a number of different mechanisms. People argue about which is most important for various types of aircraft. Some say it's all about the Bernoulli effect. Others say it's all about "pushing air down". Without being well versed in mathematics (at university level) it can be difficult to grasp even the fundamentals of these arguments. Some pilots don't understand them. My own attempts have led me to approach the problem on a number of levels, thus...
Level 1: Your Phone Bill
Hold your latest phone bill by one end (you don't have to take it out of the envelope, but it will help if you do because it will be lighter). Swoosh it horizontally through the air, cutting the air with it. If you're holding it dead straight (zero degree angle of attack) the free end will be sagging under its own weight - just like when you're holding it still.
However, if you tilt the leading edge up slightly (giving it a positive angle of attack), the free end should rise up to level - or even slightly above level with the end you're holding. You may have to swoosh quite fast to experience this - depending on how many phone calls you made last month.
What is happening?
The air is imparting a force onto the phone bill, which counteracts the force of gravity. Such a force is called lift.
When the Wright brothers were busy inventing the aeroplane, they performed this experiment repeatedly - even going to the lengths of mounting the phone bill on a spring balance in front of a fan. A more refined version of the device became known as the lift balance, which enabled them to optimise the curvature and angle of attack of the wing on their 1902 glider - the first relatively pilotable aircraft.
Level 2: Jetliners
The physics of aerodynamic lift as applied to modern jetliners goes a little bit beyond yesterday's mail - and the Wright brothers' bicycle shop, for that matter. This is because fluid dynamics is very finnicky about velocity (gases are fluids, so aerodynamics is a subset of fluid dynamics). At speeds only ten times faster than you can swoosh your phone bill, different things such as laminar flow effects start start to happen near the boundary layer (the "layer" of air that is more or less touching the surface of the wing).
The best way to begin to understand these effects is to read a bit about Reynolds' number, which is essentially a measure of the viscosity of air in various conditions.
Then you need to go on and read about Euler's Equation of Inviscid Motion, which describes the forces involved with turning a flow of something (for high values of Reynolds' number). This is where the maths gets hard. The Wright brothers would have used this equation to optimise their wing design if they had wanted to go a few hundred miles an hour.
For non-mathematical punters, a very dodgy explanation is included below. Don't take this to the science fair, but next time you find yourself on a long haul flight and can't sleep because you never quite got how a few metres of metal can hold a 400 tonne brick in mid air, it might give you just the reassurance you need to get a bit of shut-eye.
Level 3: Fire Hydrant Thought Experiment
The upshot of boundary effects is that the wing behaves more like a phone bill in front of a gushing fire hydrant than one being swooshed through air. Just go with me here for a moment...
Imagine holding your phone bill firmly (by both ends) in front of a gushing fire hydrant1, fairly close to it (say about a 30cm away) and right in the middle of the torrent of water. Probably the first thing that will happen is that the phone bill will disintegrate, which will help you to understand why aeroplanes are made of things like steel, aluminium and carbon fibre. Let's imagine that the bill is printed on strong, waxed paper that can hold up for a minute or so under the incredible force. The second thing you'll notice is that if you hold it in any orientation other than exactly parallel to the flow, the drag will just about knock you off your feet. Drag is a very big part of why the wings of jetliners are shaped the way they are.
So, using the parallel orientation as a baseline, just make very subtle adjustments. If you're a bit clever or a bit lucky, or better still if you can reshape the phone bill slightly instead of just tilting it, you'll be able to turn the flow of water. When you manage to do this, you'll experience lift in a way that's roughly analogous2 to how jetliners experience it. It will be quite strong (and probably sideways) so if you weigh less than 400 tonnes, brace yourself.
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1 Obviously, I do not recommend wasting water or endangering yourself and others by actually performing this experiment.
2 I say "roughly analagous" because the way that jetliners do it has a lot to do with pressure. You're not going to experience the Bernoulli effect (one of the boundary effects experienced by jetliners), for example, in the torrent of a gushing fire hydrant, because pressure behaves quite differently in liquids than in gases. The important thing is understanding that the wings of a jetliner are turning a flow of air, and this is what makes them work. They turn the air towards the ground, imparting a force onto it that is equal and opposite to the resultant lift force. | 
