Gender Queer can be a term to describe a gender identity that is not encompassed by traditional roles of male and female.
This could be a person whose sense of self is the opposite of their perceived gender, such as a Transgendered person who is a “Male to Female” (T to F), or “Female to Male” (F to M).
Additionally, the term can be used for someone who is poorly described by traditional labels, and also not completely described by the term “Transgendered”. Thus, someone whose sense of self is not wholly male or female, but embodies elements of each gender could also be described as Gender Queer.
A Gender Queer person might respond to a question about their gender in many, many ways. Some might say, “There are male aspects to who I am, and female aspects to who I am. I value all those aspects of my sense of self and do not want to separate myself from the different parts of who I am.” Others might be crystal clear about their sense of self relating to gender, and find that the perception of society as to their gender is frequently wrong, and be totally okay with that. Still others may be on a journey to identifying their sense of self, and be perceived as one gender or another, sometimes correctly and other days not so much.
The overarching reality is that the way of identifying as either all male or female, or M to F or F to M, has has paved the way for the current level of comfort with gender being a more fluid, and less concrete concept.