Isabella is the Duke of Brachiano's extremely unfortunate wife. She shows admirable qualities like devotion and gentleness (and even fakes searing rage against Vittoria, in order to act like she's jealous and out-of-control, sparing the Duke embarrassment)—but those aren't enough to prevent her demise. Symbolically, it's kissing a picture of her adulterous husband on the lips (as she does every day) that kills her—Brachiano has made sure that the painting has poison on it. This needs to be one of the all-time most perverted ways for someone to murder his own wife—given that it uses the other person's continued devotion as the means of death.
Although Isabella dies pretty quickly, she still gets some important lines and moments in the play. She expresses her (fake) rage at Vittoria very eloquently, for instance:
Are all these ruins of my former beauty
Laid out for a whore's triumph? (2.1)
And she also (albeit during the same charade) criticizes her lack of power in society:
O that I were a man, or that I had power
To execute my apprehended wishes
I would whip some with scorpions. (2.1)
You tell 'em, girl.