Bisexuality is one of 4 sexual orientation patterns and describes anyone whose attractions are not limited to one sex. The concept of sexual orientation was invented by the pioneers of the LGBT rights movement, all the way back in the 1860s, in their fight to decriminalize homosexual behavior. Sexual orientation terms use scientific language to describe the relationship between a person’s perceived reproductive sex and the sex(es) to which they are attracted.
Bisexuality describes a person with both homosexual (lit. same sex) and heterosexual (lit. different sex) attractions. It is an open and inclusive word that describes a diverse group of people with a wide variety of experiences around same-sex and different-sex attractions. As a scientific term, bisexual is not just an identity label; it also describes behaviors and attractions.
Identity labels like pansexual, polysexual, omnisexual, and ambisexual also describe a person with homosexual and heterosexual attractions, and therefore people who have chosen those labels are also bisexual. By replacing the prefix bi- (two, both) with pan- (all), poly- (many), omni- (all), ambi- (both, and implying ambiguity in this case), people who adopt these self-identities seek to clearly express the fact that gender does not factor into their own sexuality, or that they are specifically attracted to trans, genderqueer, and other people who may or may not fit into the mainstream gender categories of male and female. This does not mean, however, that people who identify as bisexual are fixated on traditional notions of gender.
The term fluid expresses the fact that the balance of a person's homosexual and heterosexual attractions exists in a state of flux and changes over time. Usually, but not always, people who describe their sexuality as fluid are bi people whose attractions skew very heavily towards one gender.
The terms heteroflexible and homoflexible add a further level of specificity, by indicating whether the bi person's attractions skew almost exclusively towards same-sex or different-sex individuals.