It depends on context, and even then, what does that actually mean ? Are we talking about the definition, or the thing itself ?
For those who think they can change their gender (or race) for example, try it now...try and change your gender whilst reading this. Then you realise the concept of choosing gender is sort of weird. This is different to expressing, or identifying internally (or externally) gender. This is also different to a society defining what gender (or race ) is. We can relabel things, but that doesn't change the essence of the thing itself. I can call a blue/silver dress blue or silver if I want, but the underlying essence of the dress never changed (our perception of it may do).
Is there a biological component ? Is the brain a biological component, do formed memories, synapses, genes, etc count ? I don't think that's fully known yet, but my understanding is the latest studies imply that yes there is.
I guess the main issue is self-identifying, whatever you want to call it.
On the previous page, I highlighted ambiguities that exist on all levels: biological, chromosomal, preference, and self-identity. It wasn't on-purpose but in my explanation I avoided talking in terms of changing gender, but rather the ambiguities that exist at every gender/sex related aspect.
The main complexity is when recognizing that gender is not binary. Even biologically there are 5 genders: male, female, true hermaphrodite, male pseudo-hermaphrodite, and female pseudo-hermaphrodite.
The Oxford definition talks about gender as "a range of identities", which go well beyond classic male and female genders, and include a growing list of ambiguities of mixed gender, no gender, or multiple genders -- i.e. social and cultural constructs. The WHO recognizes that "It varies from society to society and can be changed."
When we talk about changing gender, it could be a soul-searching determination that a biologically functional man "feels like a women". Or it could be more complex, it could be a change from the classic male/female dichotomy to one of a growing list gender descriptions (not very scientific, but a recent count had facebook offering 58 gender descriptions).
Stolen from wikipedia, we see a more complete list of gender determination factors:
The following gender taxonomy illustrates the kinds of diversity that have been studied and reported in medical literature. It is placed in roughly chronological order of biological and social development in the human life cycle. The earlier stages are more purely biological and the latter are more dominantly social. Causation is known to operate from chromosome to gonads, and from gonads to hormones. It is also significant from brain structure to gender identity (see Money quote above). Brain structure and processing (biological) that may explain erotic preference (social), however, is an area of ongoing research. Terminology in some areas changes quite rapidly as knowledge grows.
- chromosomes: 46,XX (genetic female); 46,XY (genetic male) ;45,X (Turner's syndrome); 47,XXY (Klinefelter syndrome); 47,XYY (XYY syndrome); 47,XXX (XXX syndrome); 48,XXYY (XXYY syndrome); 46,XX/XY mosaic; other mosaic;
- gonads: testicles; ovaries; ovarian and testicular tissues, not in same gonad (true hermaphroditism), ovotestes, or other gonadal dysgenesis;
- hormones: androgens (including testosterone, dihydrotestosterone, etc.), estrogens (including estradiol, estriol, etc.), - antiandrogens, progestogens, and others;
- primary sexual characteristics: genitals
- secondary sexual characteristics: dimorphic physical characteristics, other than primary characteristics (such as body hair, development of breasts); certain changes in brain structure due to organizing effects of sex hormones
- gender identity: one's sense of oneself as a man, woman, or gender non-conforming;
- gender expression: presentation and behaviors that express aspects of gender identity or gender role