How does the Coanda effect help some aircraft produce more lift?
According to Wikipedia, the Coandă effect causes the airflow over the top of the wing to "stick" to the upper surface of the wing and continue to hug the wing surface even as said surface curves downwards.  In normal flight, the airflow remains attached to the wing surface all the way to the trailing edge of the wing; as the upper surface of the wing's trailing edge (and, for that matter, generally the lower surface as well) is angled downward, the airflow over the wing is travelling downwards when it leaves the trailing edge, which, as per Newton's third law, produces an upwards force on the wing (and, thus, the aircraft), which we know as lift.  The An-72's overwing engine placement increases lift at low airspeeds because it causes the engine exhausts to blow over the top of the wing; the high-speed exhaust sticks to the upper surface of the wing thanx to the Coandă effect, and is thereby ultimately deflected downwards by the downwards curvature of the rear portion wing's upper surface, producing good lift even at low airspeeds.

A simple way to think about it would be that the An-72's engines blow air and hot gas downwards as well as backwards, but, instead of doing so via traditional ducting, they blow air downwards by blowing it over the top of the wing and allowing it to stick to the upper surface of the wing and follow said surface down.

Note that this is not the only, or even necessarily the primary, mechanism by which aircraft generate lift; it just happens to be the mechanism that is enhanced by the An-72's engine placement.