AirDrop for wireless only by default
By default, Apple enables AirDrop only for wireless and not for wired connections. So if you'd like to enable AirDrop for wired connections, launch up the Terminal.app (which you can find in Applications > Utilities), and then paste in one of the following two commands.
Command for only the logged-in user
Command for all users
You may have some luck relaunching Finder, but I'd recommend rebooting your computer entirely, particularly if you're changing the setting for all users, and not just the logged-in one.