2 Answers

Complicated question : Type Airfoil explanation in Google and start reading there . Then look up Bernoulli  principle Then there is lift trust and drag to understand .This will get you started. Hope you enjoy your journey.

very complicated:  Bluesman is right, this question of flight has been around since man's beginning and only understood in the last 120 years.  Once understood, it all makes simple sense.

Quick answer is thrust pushing the airplane forward forces air over the wings to lift the wing causing the airplane to fly.. To understand 'airfoil' in simple terms, put your hand out of the window on a moving car and see how you can 'fly' your hand by moving your hand up and down (twist your wrist)