Have you ever read a story where nothing goes wrong? It would be pretty boring. A day where everything is perfect makes a nice life, but a sleepy story. Stories need a bump in the road to get interesting.
The problem is the engine of a story. An engine is the part that makes a car go, and the problem is the part that makes a story go. Until something goes wrong, the characters just sit around and nothing happens.
A problem is when a character wants something but there is trouble in the way. A dog wants his bone but it is stuck under the couch. A girl wants to win the race but she trips at the start. That trouble is what pulls the reader in.
The solution is how the character solves the problem. It is the moment things finally work out. The dog nudges the bone free with his nose, or the girl gets back up and runs her hardest. A good solution makes the reader feel happy or proud.
The best solutions come from the characters themselves, not from magic or luck. When a character uses her own brain and bravery to fix the trouble, the ending feels earned. That is why nothing interesting happens until something goes wrong.
You can spot problems and solutions in almost every story, movie, and game. Next time you read, pause and ask what the character wants and what is standing in the way. Finding the problem helps you understand the whole story.