There is a grade-school explanation of how a wing works that goes approximately like this (although I'm leaving out an erroneous bit):
Because of the geometry of the way the wing meets the air, air accelerates as it goes over the top of the wing. There is something called Bernoulli's Principle that says that the pressure of a fluid decreases as its velocity increases. Because the pressure against the top is less than the pressure against the bottom, there is lift.
The oft-included erroneous bit is a claim about why the air speeds up over the top. The claim is that the air along the top has to make it over in the same length of time that it would have taken to go along the bottom. Since it has a longer trip over the top, the story goes, it has to go faster. This is not the right reason at all. There is no rule of equal transit time and, in fact, the air along the top of the wing takes less time to get to the trailing edge.
People often point to that error and say it shows that the Bernoulli effect is not a correct explanation for flight. For instance, this question makes the assertion that the Bernoulli effect is "at best a minor contribution to the actual lift", and none of the answers contradict this. But seems to me that the true situation only makes the Bernoulli effect even more important, because the acceleration of the air stream is greater than you would think if you believed the equal-transit-times story. Why is this wrong?
I also hear that it isn't the Bernoulli effect, it's that the wings redirect the air downwards. But it does not seem to me that those two explanations are mutually contradictory. If they are, I would like to understand that as well.