Legend Score is a way to quantify how much you've done in CW Flyff. It's awarded for killing monsters, clearing dungeons, finishing quests, and completing achievements. See Details: Legend Score for specifics about how much you get per activity.
You can see your Legend Score on your character window (Default Hotkey: T), right under your experience bar.
On the Season server, Legend Score determines which tier rewards you get, with higher Legend Scores netting you rare and unique fashion.
For both Season and main (Clockworks), Legend Score is also shown on the CW Flyff website, under Player Rankings.