Dry-aged beef is hung in a room where it's exposed so the juices on the outside of the meat can evaporate. Wet-aged beef is wrapped in plastic so the juices are retained.

Dry-aged is often more tender and has a stronger beef flavor, as the moisture (flavorless water) is allowed to evaporate, leaving behind the delicious delicious meat. It's also more expensive to dry age, as you can't just vacuum-seal it up and stick it in a fridge and forget about it for a few weeks.