Fairylights are recurring alien-like monsters; they are usually serving as early to mid game monsters. Their appearance in the first game was much different than their later appearances, but have been more or less consistent ever since Wild Arms 2.
Fairylights usually are not too much of a threat, as half the time they will idle. But even so, they should not be underestimated, as they can be dangerous to an unwary player, especially since they can cast strong light magic in some cases. In later games, they are more of a threat, since they do not idle, and can use skills such as Hyperion Blaster.