Biologically, a woman is a human with two X chromosomes. This would be the best scientific answer I would give if someone asked me that question.
Socially, a person can choose to be perceived in any role they wish and which is accepted by those around them -- or not! In other words, social gender roles like other roles are varied around the world and over time. If someone feels more comfortable in a different role, I'm certainly ok with that.
I don't think one is able to change one's biological status but society has accepted that people can live in a different role than their biological status.
* Edit: I should add that I have two trans family members.