Ok kiddo, so let's start with the basics. You know that light is made up of little particles called photons, right?
Well, when a bunch of these photons come out of a special kind of material together, they can sometimes start bouncing back and forth and causing each other to get even more excited. This is kind of like when your friends get really hyped up when they're all together.
Eventually, when there are enough of these excited photons, they all "spontaneously" jump out of the material at the same time, like a bunch of popcorn kernels popping all at once. This is called "spontaneous emission".
But sometimes, instead of just jumping out all at once, these excited photons can get even more excited and start bouncing around in a feedback loop. This feedback loop makes the photons even more excited, which makes them bounce around even more, which makes them even more excited...you get the idea.
Eventually, this feedback loop builds up so much that the photons all jump out at once, but this time they're even more powerful because they're all bouncing around in sync. This is called "amplified spontaneous emission", or ASE for short.
Think of it like a group of excited kids at a party. When they're all just talking and having fun, it's just spontaneous emission. But if they start getting really wild and bouncing around together, they can amplify each other's excitement until it's a crazy, unstoppable party. That's basically what happens with amplified spontaneous emission.