Rosalind and Celia have grown up together and have formed a strong attachment. Rosalind has the much stronger character. She is more intelligent than Celia and also more self-reliant, enterprising, and resourceful. Celia is dependent and submissive. Rosalind makes a good leader and Celia a good follower. It is not surprising that it is Rosalind who decides to disguise herself as a man when the two flee from Celia's father's palace to the Forest of Arden. Rosalind also shows herself to be more assertive when she encounters Orlando. She is already in love with him but feels obliged to maintain her masculine disguise because she is acting as Celia's protector. Rosalind displays her cleverness in her battles of wit with Orlando in Act 3, Scene 2 and elsewhere thereafter.
Rosalind is peremptorily banished from her uncle Duke Frederick's court because he perceives that she outshines his own daughter Celia. He tells his daughter:
She is too subtle for thee; and her smoothness,
Her very silence and her patience
Speak to the people, and they pity her.
Thou art a fool: she robs thee of thy name;
And thou wilt show more bright and seem more virtuous
When she is gone. Then open not thy lips:
Firm and irrevocable is my doom
Which I have pass'd upon her; she is banish'd.
Since Duke Frederick has no sons to inherit the estate he has usurped from Rosalind's father, called Duke Senior, it is important to Duke Frederick that his daughter should be strong, self-confident, and decisive rather than passive and dependent. Celia cannot change to please her father. She is totally devoted to Rosalind and promises her that when her father dies she will relinquish his estate to her. When Rosalind is banished from the court, Celia gives up everything in order to accompany her friend into exile. Rosalind never displays any ulterior motive in her friendship with Celia. She loves Celia just as much as Celia loves her.
Shakespeare had a practical purpose for stressing the friendship between Rosalind and Celia. In almost any play there must be at least two characters on the stage because all the information is conveyed through dialogue. Rosalind has to be able to tell somebody what she is thinking, what she is planning, etc. This is actually the main reason why Celia accompanies her into exile. Shakespeare solves a similar problem with Orlando by having the devoted family servant Adam accompany him to the Forest of Arden. Once Rosalind and Orlando are actually in the forest, the importance of the roles of Celia and Adam diminish and the relationship between Rosalind and Orlando takes center stage.
In Shakespeare's Hamlet, the Prince is often seen by himself. He engages in long soliloquies to let the audience know what he is thinking, feeling, and planning. But this is a little awkward. Typically Shakespeare has to bring two characters together in order to advance his play. A good example is the many conferences between Macbeth and his wife. Dialogue is the heart and soul of stage plays. It is interesting to observe the combinations of characters Shakespeare creates for the purpose of having them talk to each other. Even in Hamlet he has the Prince talking to his father's ghost, to Polonius, to Ophelia, to Gertrude, to Laertes, to Horatio, to Rosencrantz and Guildenstern, and to many others.
Celia is not a strong character. She exists mainly to give Rosalind someone to talk to, just as Horatio exists mainly to give Hamlet someone to confide in.