This answer is based almost entirely on my own experience as a gay man in his late twenties in the UK, so sorry for the lack of references. You will see many other interpretations of the terms you've asked about, so take any view with a pinch of salt.
First of all, let me say that there are many variations on the "LGBT" acronym, and there's always disagreement on it within the LGBT community. It's been changing for as long as I've known it. On the whole, the trend seems to be that it becomes more inclusive of different groups as time goes on. Here are a few letters you might see in it, and some of their meanings:
L = lesbian
G = gay
B = bisexual
T = trans (sometimes transgender, sometimes transsexual)
Q = queer (or questioning)
I = intersex
U = undetermined, undecided
A = asexual (sometimes ally)
N = non-binary
The most common acronyms are probably LGBT, LGBTQ, and LGBT+ (where the + is a catchall for other groups). The most complicated variation I've seen used semi-seriously is "QUILTBAG".
Here's some more information about how the acronym has expanded (which includes some terms I haven't associated with the acronym before and so haven't mentioned above): https://www.pinknews.co.uk/2017/11/06/how-has-the-lgbt-acronym-evolved/
I'm going to use LGBT+ throughout this answer as a general term.
Now to answer your specific questions:
Is it distinct from gay or Lesbian? If so, why?
It can be. Some people don't feel that they fit into labels like lesbian or gay, for a number of possible reasons, including:
These terms are narrow, and are typically understood as narrow categories for exclusively gay people (i.e. men who are exclusively romantically interested in men, or women exclusively romantically interested in women). Some people may feel that their sexual orientation does not fit neatly into one of these categories.
They disagree with the idea of narrow labels, so prefer a more all-encompassing term. For example, Some people feel that dividing and subdividing the LGBT+ community is unhelpful, perhaps because they feel that solidarity within a minority group is important, so they choose a label that connects the members of the group rather than dividing them into separate camps.
They don't agree with some of the connotations of these terms. Gay and lesbian have been used as the primary terms for homosexual men and women for some time now, and have a set of deeply rooted connotations based on their use, the portrayal of "gay" and "lesbian" people in media, etc. Some people may not want to be associated with those connotations, and prefer to choose a term that has different connotations (or, for many people, fewer deeply formed connotations), which they perceive to more closely fit their identity.
...and no doubt many other reasons besides those three.
Has "queer" as a banner term been appropriated by another group, or been jettisoned by the larger LGBT community?
Not that I'm aware of. However, many LGBT+ people don't identify as queer and don't use the term queer to refer to the LGBT+ community, which is part of why you'll often see it omitted or see other terms instead.
My impression is that it's gaining acceptance as an umbrella term for LGBT+, but has yet to achieve widespread acceptance and adoption.
Does it have something to do with bisexuality? If not, why is it grouped there?
Some people who are attracted to both men and women might identify as queer in addition to or in preference to identifying as bisexual. It may be more common among bisexual people because the term 'bisexual' has negative connotations or evokes stereotypes among some people, even within the LGBT+ community (for example, some people hold the view that bisexuality doesn't really exist, that bisexuals are just gay people who won't admit it, that bisexuality means being equally interested in men and women, etc.) For this reason, people may prefer a term that they consider to have fewer such connotations, and may prefer queer.
However, I think it's odd that they grouped bisexual and queer together in one answer. Most people wouldn't equate these two things as being the same, and some people might be offended by the idea of lumping different terms into one category.
Does it mean something else? If so, what?
Hopefully the above has already explained this. Some people would say that queer can refer generally to any of the things I've mentioned above (all of the LGBTQIUAN+ identities) and probably to some other identities that I've forgotten to include.
Finally, to give you some real authority, rather than just my opinion, here's how Stonewall defines queer in their online glossary:
Queer – in the past a derogatory term for LGBT individuals. The term has now been reclaimed by LGBT young people in particular who don’t identify with traditional categories around gender identity and sexual orientation but is still viewed to be derogatory by some.
-- Stonewall's Glossary of terms
You may find some of the other definitions in that glossary interesting too.