Imagine you are playing a game with blocks. You have different shaped blocks you can use to build a tower. Normally, you will use the blocks that fit easily together to make your tower.
But sometimes, you might find a block that is a different shape and doesn't fit so easily with the others. This is like a corner case. It's a situation that doesn't happen very often or it's a special case that needs extra attention.
Just like you might need to stop and figure out how to add the odd-shaped block to your tower, when people are designing programs or systems, they need to think about these unusual situations. They need to make sure that their program can handle the corner cases in order to work properly.