What is significant that offered changes her feeling of commit suicide after she knows Nick in The Handmaid's Tale?
I think you are asking, "Why is it significant that Offred changes her mind about the act of suicide after she knows Nick?"
If so, then the reason she changes her mind and starts the see the world as a less hopeless place is because she has a more genuine human connection with Nick, more like the way things used to be before the regime change and the creation of Gilead. Nick is someone with whom is CHOOSING to be with in a sexual way and for their mutual pleasure. He is more like her husband than the pseudo-relationship she has with the Commander. While the Commander is tyring to connect in a more personal way than the ceremony, it is just not the same.
Because she has this connection with Nick she thinks that life is more worth living. Suicide is a running theme through the novel -- the handmaid prior to Offred killed herself in the very room Offred now occupies. The new life seems hopeless, dangerous and degrading, especially to Offred and this "first generation" of handmaids who remember how it was before. Suicide was a way out of what seemed inconceivable and allowed a woman to take control of her situation, as opposed to letting this chauvinistic regime take all of the power and control. Being with Nick makes her see that she can have some control and pleasure back.