One of the main functions of Halcyona is as a battleground for the World PvP event The War for Halcyona. It also has a prolonged peace period, which makes it an ideal location to begin Trade Routes from.
Points of Interest
If you feel like exploring, check out that cool crane by the Airship Laboratory. Glide over, stand on top of the furthest point, throw your fists in the air, and shout about your grand accomplishment. Don't fall, though. You will almost certainly die.