It is a word which has been reappropriated by social and political LGBT rights activists, and is the word which a lot of academic studies use to describe non-heterosexual identities. It is also used as a word which talks about someone's sexuality or gender in a deliberately non-specific way.
Queer is mostly used by younger LGBT people to describe themselves and is usually described as a "fluid" label. Many people like the term in the LGBT community as it focuses on what that community has in common and not its differences. But many older LGBT people may find the term "queer" to be offensive due to its use as a homophobic insult. Some queer folks may or may not be genderqueer (of non-binary gender).
The term "queer" entered English in the 16th century, meaning strange or a word describing someone who is sick. The word was used a lot in the 20th century to refer to gay men, as it still does a lot today.