In its simplest definition, transgender refers to a person whose gender identity is not the same as the sex assigned at birth. They may not support the assigned gender roles associated with their birth gender (or with any gender).
More About Transgender
The definition of transgender is rather fluid, but in its essence, it describes someone who does not conform to society's gender roles.
Identifying as transgender is not related to a person's sexual orientation. Trans individuals may identify as heterosexual, homosexual, bisexual, etc. Transgender identity can be expressed in many ways, such as transsexual (identifying as a member of the opposite sex), cross-dressing, genderqueer (gender identities outside of man or woman), androgyny, or bi-gender.