How does carrying work when you add big numbers?

You're stacking two big numbers on top of each other, ready to add. The ones line up, the tens line up, the hundreds line up — a tidy little tower. Then somewhere in the middle, a column adds up to more than nine, and suddenly there's a leftover digit with nowhere to sit. That leftover is what carrying is all about.
Here's the secret rule that makes carrying necessary: each spot in a number can only hold a single digit, zero through nine. The ones place, the tens place, the hundreds place — they're like little boxes, and each box fits exactly one number. The moment a sum tries to cram a ten-or-bigger into one box, something has to give.
