The meaning of 'Claire'

It's also the feminine form of the French adjective "clair," which means "light" (in the sense of appearing light in color).

For example:

Il porte un pantelon bleu clair - He is wearing a pair of light blue pants
Il porte une chemise bleue claire - He is wearing a light blue shirt.

"Clair" also doubles as a noun that means "light" (in the general sense of the word--not a specific source of light, such as a lamp or the sun).

For example:

le clair de la lune - the light of the moon; moonlight

So, Claire is the light of RE.