Luggage is anything you use to carry your things with you on a trip. If you're backpacking across Asia, your only luggage is the pack on your back.
Suitcases are luggage, and if you pack a trunk full of gifts to bring your family in India, that's luggage too. When you arrive at an airport after a flight, you might have to wait a while to pick up your checked luggage. Luggage comes from lug, or "drag," the way you sometimes have to lug your luggage onto a train or bus.