Okay, so first we need to understand what a laser is. A laser is like a really special flashlight that uses light to make a very specific kind of beam that's really strong and can go really far.
Now, the "active laser medium" part is about what's inside the laser. In order to make that strong beam of light, you need something called a "medium" to help the light bounce back and forth and get stronger before it comes out of the laser.
The "active" part means that this medium is special because it's actually doing something while the light is bouncing around. It's not just sitting there waiting for the light to do all the work.
Imagine you're playing soccer and you're bouncing a ball between you and your friend. If your friend just stands there, the ball won't go very far. But if your friend kicks the ball back, it will start going faster and farther each time you pass it back and forth. That's kind of what the active laser medium is doing with the light in the laser. It's helping the light become stronger and more powerful as it bounces around inside the laser.
So, to sum it up: an active laser medium is a special material inside a laser that helps the light bounce back and forth and get stronger before coming out of the laser, and it's "active" because it's doing something to make the light stronger while it's bouncing around.