First of all, Act I, Scene I of As You Like It explains that Rosalind and Celia are cousins. Celia explains that Rosalind's father is her own uncle and that her father is Rosalind's uncle:
If my uncle, thy banished father,
had banished thy uncle, the duke my father,
In other words, the two men are brothers. This is why the banished and exiled Duke, Rosalind's father and Celia's uncle, is called Duke Senior: He is the elder brother and the one who should by rights be ruling the dukedom over which Celia's father (Rosalind's uncle), Duke Frederick, rules instead.
Secondly, Rosalind and Celia are the best of friends. In other eras, there was not the present day social squeamishness over proclaiming love for friends and family--or for considering family members friends (though, as Oliver and Orlando prove, love and friendship in families was not universal). Rosalind and Celia love each deeply as friends and cousins, and both young ladies are very interested in the opposite sex and propose a game of flirtation to lift Rosalind's spirits, though Celia cautions that games of flirtation must end with maidenly blushes intact:
with safety of a pure blush thou mayst in honour come off [the sport field] again.
Two lines that Celia speaks are hard to analyze and may cause some contemporary readers difficulty. The first is that Celia says, "make [sport] withal: but love no man in good earnest." The traditional and most obvious reading of this is that Rosalind and Celia are still young, in their teens, and are not ready to fall love in earnest because of youthfulness. The second is when Rosalind tells Orlando that in winning the wrestling match, he won her heart, too, and Celia responds with "Will you go, coz?"
Sir, you have wrestled well and overthrown
More than your enemies.
Will you go, coz?
The traditional and most obvious reading is that, after just having jokingly bantered about playing at love but not loving in earnest, Celia is shocked that Rosalind suddenly falls in love with a wrestler she has only just seen--and then confesses it--out loud!