Gender variant is a broad term that refers to people whose gender does not fit with social or cultural expectations of their sex as it was assigned at birth. Gender variance doesn't necessarily mean that an individual wants to change some aspect of their body or how they look, sound, or move through the world. It is used to identify and acknowledge that some people's presentation doesn't fit what others expect. Some people identify themselves as gender variant, but it's also a term that is applied to gender non-conforming children.
The term sounds vaguely clinical or medical, but gender variance is not a medical problem or a pathology. Some people prefer the term gender non-conforming, as it sounds less clinical. Those terms are usually used interchangeably. The term genderqueer also has some things in common with gender variant, although they are not usually used interchangeably.