Alright, let's give it a go! Imagine you've got a magic notebook (Bitcoin ledger) that everyone in class can write in. But once something is written, it can't be erased or changed.
Now, imagine we've got marbles (bitcoins). You tell the whole class when you give some of your marbles to another kid. You write down how many marbles are moved and who's getting them in our magic notebook.
This is all pretty simple, right? Now here comes calculus part: solving complex puzzles (mining). It's like being the fastest kid to finish a super hard Sudoku puzzle gets to decide what goes into the notebook next and gets some new marbles as reward!
This is basically what Bitcoin does - but instead of kids and classrooms we have computers and internet!