The character of Medea in this play is very quickly established as a figure who is both an outsider in that she does not belong in Corinth, and also as a barbarian through the extent of her passions and how she is willing to act on them. Note how in the opening speech of the play, the Nurse describes her mistress as having forsaken her father, her land and her home for the love of Jason:
...all alone she moans the name
Of father, and land, and home, forsook that day
For this man's sake, who casteth her away.
It is clear that Media sacrificed her homeland and family to follow Jason out of love, and now Jason has responded by leaving her for a better proposition in order to secure his own rise to power. She is depicted therefore at the beginning of the play as an exile who does not belong in Corinth, who also has abandoned her homeland for love of Jason, the man who has in turn abandoned her.
At the same time, however, it is clear that she is not just depicted as an exile or an outsider, but also as a barbarian, who has passions and emotions that result in terrible actions. Note what the Nurse says about her mistress in the following quote:
Methinks she hath a dread, not joy, to see
Her children near. 'Tis this that maketh me
Most tremble, lest she do I know not what.
Her heart is no light thing, and useth not
To brook much wrong. I know that woman, aye,
And dread her!
The fact that "her heart is no light thing" and that she is not able to "brook much wrong" hints at her excessive revenge when she is inspired to act. The Nurse even goes as far as to say that she "dreads" her mistress and the acts that she is capable of committing. This of course foreshadows the tragic ending of the play, but also hints at the barbarian nature of Medea. It is clear therefore that very early on in the play Medea is established as a woman who is both does not belong in Corinth but also somebody who is a barbarian and therefore acts in ways unthought of within their civilised society.