An airfoil isthe cross section of the wing of an aircraft. The most basic airfoil (and the first studied in elementary aerodynamics) is simply a circle, representing a cylinder. To get lift, the cylinder is rotated. Generally speaking an airfoil can be any 2D closed profile, but try flying a 30 meter wide pickup truck.
More practically, an airfoil consists of a rounded leading edge, a gently curving section in the middle, and back to a sharp trailing edge. It looks something like this:
Thanks to sekicho; ASCII art as seen on aircraft.
A symmetric airfoil will produce lift at small, positive angles of attack, while a cambered airfoil will produce lift at anywhere from a slightly negative angle of attack to a small positive angle of attack.
Airfoils designed for supersonic flight are significantly different, typically having sharp leading edges and a very small thickness ratio (the ratio of thickness to chord). This keeps the shock wave attached and reduces drag.