Ismene is incredibly important to the play. For one thing, she acts as a foil to Antigone. In literary terms, a foil is someone who provides a contrast with another character, usually the protagonist, in order to highlight particular qualities of that character. In this case, the protagonist is, of course, Ismene's sister, Antigone.

Ismene, unlike her sister, is not a dynamic character; she remains the same throughout the entirety of the play. She doesn't make things happen—things happen to her. Nevertheless, she still has an important role to play, and not just as a foil to Antigone. Ismene, no less than Creon, represents the forces of human law and convention. Antigone, by contrast, is openly prepared to defy Creon and all that he represents, in order to do what's right by all that's just and holy. Furthermore, in defying Creon, Antigone is also displaying her contempt for Ismene for her unthinking submission to Creon's will, a mere earthly power. After all, Polynices was Ismene's brother too, so to some extent we can understand Antigone's hostility towards her sister.

At the same time, however, Ismene strikes us as a sympathetic character overall. For one thing, she's very much a creature of her time, a woman living in an age when women were expected to be meek, demure, and submissive to their menfolk. There's nothing unusual or especially cowardly about her actions. Indeed, the vast majority of women at the time would've done the exact same thing. But because Antigone displays such extraordinary heroism, we're in danger of overlooking the harsh realities of the time.

Finally, Ismene gives us someone in the play with whom we can identify more readily. She confronts us with a stark challenge: what would we have done in her shoes? Although we can still admire Antigone's enormous courage, there's still something almost godlike about it, something that we can't imagine ourselves doing, save for in exceptional circumstances. Ismene, for good or ill, is only human, and as such provides an essential dramatic counterpoint to the superhuman courage of her sister.

I suppose I have to disagree with the previous post.  Indeed, while I feel she is a minor character, I think that Ismene operates on several essential levels in the play.  One reason why I think she is important is that she displays another side to the predicament of being a woman in Greek times.  While Antigone is quite committed to breaking Creon's unjust laws, Ismene reminds her sister of what the expectations are for a woman and the importance in following this convention.  It is essential that Ismene voices this point of view, as women did have to deal with a different reality (and still do, to a large extent) than the men did.  Antigone's dilemma is enhanced because of being a woman, and having to wrestle with the cultural reality that frowns upon independent thought of a woman countering patriarchal laws.  Ismene also operates on the level of what happens when passivity and...

What is Ismene's main purpose in Sophocles' Antigone?