For a variety of opinions about "Celtic Woman," check out:

this thread

As you'll observe, it's not one "woman" (singluar), but a group of very attractive young women whose musical talents are the subject of some debate, best known for videotaped concert appearances shown on PBS (American public TV) during fund-raising drives. Depending upon whose option you trust, their presentation is either overproduced and tastelessly commercial, or beautiful and inspiring.

(My own opinion falls somewhere between the extremes. I've never watched an entire program; I think the ladies are undoubtedly talented, and the music mostly quite enjoyable, but that the show as a whole is quite deliberately middlebrow, directed toward the largest possible audience.)

Describing "She Moved Through the Fair" as a "Celtic Woman song" is probably a demeaning dismissal of a song that can be quite wonderful when presented by the right perfomer, and which certainly predates the CW group's formation, regardless of whether it's truly ancient or if it was composed only a single century ago.