What is this "flap-like" thing on the back of the F-15?
It is a speed brake (air brake). Here is a closeup of it.



Image from aero-cafe.com

It is usually used reducing speed landing (approach). It is also used for other functions- to slow down quickly at high speeds and to prevent too much speed buildup in a dive.

This image shows it being used during approach.



"F-15A 21st TFW landing with extended speed brake 1984" by SSgt. K. Vail, USAF - U.S. DefenseImagery photo VIRIN: DF-ST-85-11671. Licensed under Public Domain via Wikimedia Commons.

Similar airbrakes are also found in other aircraft, notably the Su 27 and its derivatives.



Image from aerospaceweb.org