Imagine you are in a boat on the ocean. The horizon is the line where the sky meets the sea. The horizon is as far as you can see. Literally, if you see something on the horizon, it is far away and yet you can see that it is there. Figuratively, "on the horizon" can mean "as far as you can see into the future." "I see trouble on the horizon" means "I am certain there will be trouble, even though it won't happen immediately." Here are some examples of use. "The government is spending too much. Everything seems all right now, but there is trouble on the horizon." "That company's stock is rising, but they are facing competition they have never faced before, and I see trouble on the horizon." Here's an actual headline: "Tesla's new Model 3 sedan has test drivers swooning — but quality issues lurk on the horizon."

It means you anticipate trouble. You believe a problem will occur. The horizon is the line where the earth meets they sky, so it means if you are looking ahead you sense the future. An example sentence could be "I see touble in the horizon for Suzanne because she is dating a man that flirts with too many women."