Corroboration means having a bunch of clues that all fit together and tell the same story.
Let's imagine that you came home from school and your parents see that your backpack is missing. You tell them that you left it at school by accident, but they're not sure if you're telling the truth or not.
To corroborate your story, they might ask your teacher if you left your backpack in class, they might check the school's lost and found for your backpack or they might ask your classmates if they saw you leave with your backpack.
If all these clues point towards the same story - that you left your backpack at school - then your story is corroborated.
When it comes to things like solving crimes or making big decisions, corroborating evidence helps make sure we're getting the whole picture and making the best choices.