Okay kiddo, let me explain what a drilling stabilizer is in a way you'll understand. You know when you're trying to draw a straight line with a pencil and your hand shakes a little bit? Well, that can make the line wiggly and not straight.
The same thing happens when drilling for oil or gas underground. The drill bit can wobble and make the hole not straight. This is a problem because the drill needs to go straight down to reach the oil or gas.
That's where the drilling stabilizer comes in! It's kind of like a weight that gets attached to the drill stem (that's the long thing that connects the drill bit to the machine that's drilling). The stabilizer helps keep the drill bit steady and straight, so it can make a nice straight hole.
Just like how you hold a heavy backpack close to your body to keep it balanced, the drilling stabilizer works to keep the drill bit balanced and the hole straight. And that's how a drilling stabilizer helps with oil and gas drilling!