To haul is to move or take something, usually big and heavy, and put it somewhere else. If you've ever moved to a new house, then you know that having to haul all your stuff there can really take the joy out of moving into a new place.
You'll want to reserve haul for situations in which carrying something takes a lot of effort and ain't a lot of fun. You don't haul a sack of feathers, for example. You haul a bag of boulders, or a box of books. Haul is usually a verb, but you can also use it as a noun, when you're talking about lot of something that you caught or won. We went digging for clams—look at our haul! After winning at blackjack, take your haul and hit the road. Don't risk losing it all on roulette.