“Do you see that thing floating out there on the horizon?”
You're at the beach. You see something far out in the ocean. You're not sure what it is because it's really far away. You point it out to your friend.
Do you see that thing floating out there on the horizon?
If you see an object in an ocean, lake, or large river which is a bit far, you can say that it's "out" somewhere:
I saw a little fishing boat out off the shore a few minutes ago.
Hey, you're out too far! Come back in.
We were thinking about taking the catamaran out on the lake. Want to come?
The "horizon" is the line where the sky and the earth seem to meet each other when you are looking at the ocean or a flat area of ground.
When you look at something large that's very far away, it might look like it is touching this line. In that case, you can say that it is "on the horizon":
I see something on the horizon.
People also use the phrase "on the horizon" in a figurative way. They use it to talk about something that's going to happen in the near future. For example:
We have some interesting new projects on the horizon.