An umbrella term is a word or phrase that covers a broad range of related things that are different from each other but all belong to the same category. Bisexuality is an umbrella term that covers a wide range of identities, terms, attractions, and behaviors that all fit the scientific definition of bisexuality.
Just as there are millions of ways to be straight, gay, lesbian, or asexual, there are as many ways to be bi as there are bi people. No one word can fully capture the nuances of personality, culture, beliefs, or personal preference; no word should try to. The term bisexuality makes no such pretense - it is a general and inclusive term that encompasses everyone: all sexes and all genders. That does not mean that bi people are attracted to everyone, merely that bi people’s attractions aren’t limited by sex or gender.
Terms that fall under the bi umbrella include pansexual (attraction to all genders, with a political emphasis on nonbinary gender identities), polysexual (attraction to multiple sexes), omnisexual (attraction to all sexes), and multisexual (attraction to multiple sexes). Some people prefer the term fluid meaning that their attractions are not fixed and include people of more than one sex over time. Some people feel that their sexuality, while not limited by sex or gender, is best left unlabeled because it is not central to their sense of self. If these terms all seem to mean the same thing, that is because they basically do! Still, these words have value in that they allow people to describe their sexuality in ways that feel more comfortable or precise. They allow people to express their identity; how they see and understand themselves and want to be seen by others.
It’s helpful to note that while anyone who experiences both homosexual (same sex) and heterosexual (different sex) attractions is bisexual according to the scientific definition, that does not mean that they will label themselves or even think of themselves (identify) as bi.