Okay kiddo, you know how sometimes you make a mess at home and you can't just throw it in the trash can because it's too big or too smelly? Sometimes grown-ups have the same problem with special kinds of waste that can't be thrown away like regular trash.
So, what they do is dig a long, deep hole in the ground and put the waste in it. But they don't just leave it there, they close it up really tight with rocks and special material to make sure it doesn't hurt anyone or harm the environment.
Now, sometimes this hole can be very far away from where the waste came from. That's where horizontal drillhole disposal comes in. Instead of just digging straight down, the grown-ups drill a hole that goes sideways underground, like a tunnel. They put the waste in this tunnel and then close it up really tight just like before.
This way, they don't have to dig a big hole right next to where people live, and the waste stays underground where it won't hurt anyone or anything.
Does that make sense, kiddo?