Celia is a virtuous princess, the daughter of Duke Frederick, who is devoted, intelligent, feeling, compassionate and opposed to harm being done to others, like in Charles' wrestling matches (which explains why she doesn't fall in love with Orlando herself). Her role is important in As You Like It because Shakespeare use her to explore pure and devoted love between women who feel toward each other as sisters feel.
Celia contrasts to Rosalind in several important ways that help to reveal Rosalind's qualities. For instance, Celia protests against the wrestling match as being too delicate to see such brutality, whereas Rosalind wants to see the match even though she heard the same stories of brutality. This points out Rosalind's less delicate side, making her more able to rule and establish harmony, as her role as her father's daughter would require, had Duke Frederick not stolen the throne from him. Celia also is important in revealing Rosalind's maidenly romantic side which is revealed in Arden forest when Celia tells Rosalind that Orlando is the forest poet and Rosalind gets all giddy and worries about her man's clothing.