If you click on the box, you will hear "josei," which is the first word Google Translator gives for "woman," along with plain 女, and 女の人, and four others ... I do not know the different ways they are used.
Why can't you just say 女性です。or 男性です。? I noticed that duolingo was requiring the fuller expression: 私は一人。。。before the gender, but not so for the previous ways to say I am a man or woman. Is this fuller pattern required with 女性 and 男性 ?