When you solve a problem, you find a way to fix it and make it better. When you solve a puzzle, a crime, or a mystery, you figure it out. So, a solution is a way to fix or figure out a problem. You can find or create a solution for any kind of problem or difficulty.
When the sink breaks, Bart solves that problem. He takes it apart, and removes a toy that had been jammed into the pipe. He found a good solution!
This dog has a problem: his stick is too big, so he can't cross the bridge. What's his solution? He turns the stick sideways. That's a smart dog--and a smart solution.