Other forms: figuring out; figures out
To figure out is to investigate or think something through in order to understand it. You might figure out through a little online sleuthing that your kindergarten teacher moved to Alaska and became a salmon fisherman.
You can figure out the answer to a tricky math problem using a calculator, and you can figure out how old you were when you visited Disney World by looking at photographs and consulting your parents. This informal phrase comes in handy whether you're finding the solution for a big problem or simply puzzling out something small, like when you figure out which kind of treat your dog likes best.