A solution is all about solving or dissolving. If you find an answer to a question, both the answer and how you got there is the solution. If you dissolve a solid into a liquid, you've created a different kind of solution.
This noun descends from Middle English solucion, from Old French, from Latin solutio, from solvere "to loosen." Think of solution both as a loosening of the chemical bonds that make something solid––when you loosen the structure of salt by mixing it into water, you create a solution. When you loosen the "knot" of a math problem you do the same thing––you loosen, untangle or solve it.