I've always wondered this after getting introduced to fighter jets, the sheer concept of being able to create a larger "exhaust" out of a fighter jet and cause it to speed up has always just not made sense in my brain. I was wondering if anyone could provide an easier-to-understand answer since most of the answers I've gotten from friends and family don't make that much sense to me. Thanks to anyone who can help me with this.
The hot, fast-moving exhaust from a turbojet contains lots of excess oxygen with which more fuel could be burned, if you wanted to. And with no turbine wheel(s) immersed in that superhot exhaust (downstream of the last turbine stage) you can go ahead and spray in more fuel, heat the exhaust up even more, causing it to expand and accelerate even faster out the exhaust nozzle, thereby generating extra thrust.
In terms of thermodynamic power-extraction cycles, afterburning is called reheat.