According to the story "The Necklace," what makes women important?
Within the setting of this story in the late 1800's a woman is more "important" as the question asks--meaning given more consideration--if she has a dowry and social connections; in other words, money and social status.
The lack of a dowry and "prospects, no way of any kind of being met" are what preclude Matilde's marriage to someone of a high social position. Consequently, she marries a minor clerk in the Ministry of Education. This marriage is one that she feels is beneath her because her "beauty, grace and charm" should elevate her. As a result, she feels that she has been wronged since she is meant for a different kind of life: "She longed to please, be envied, be fascinating and sought after."
When she is given the opportunity to attend a ball where the prestigious people, who would have been "prospects," are present, Matilde Loisel is finally happy. However, this contentment is only temporal as the evening ends badly. For, she has lost what she believes is a diamond necklace, a necklace she has borrowed from a former school friend. Her importance was a mere illusion.