To lug something is to drag or haul it. If you have to lug a heavy backpack to school, look into buying a fashionable backpack on wheels.
If you overpack for a trip, you might end up having to lug your suitcases around the airport, and if your grocery bag breaks on your way home, you'll have to lug your gallon of milk and bunches of bananas in your arms instead. As a noun, lug has several less common meanings, including "a handle-like projection," and "an asymmetrical four-sized sail." Informally, a lug is also an ear in Scotland, and a bully in North America.