A bear is a type of guy. Its precise meaning varies, but the general idea is large (either with fat or muscle—typically a mix of both) and covered in hair. According to Wikipedia, hairy men of any build were referred to as bears until the terms "otter" and "wolf" arose to describe men of medium and slim builds. According to The Advocate, they coined the term in 1979, although it can be said for certain that the term gained traction in the 1980s, with the creation of Bear Magazine, the founding of bear groups, and the like.

In 1995, the International Bear Brotherhood flag came to be. I only knew of this flag until now because of a sidenote in Gengoroh Tagame's genuinely excellent (and family friendly, unlike his other stuff) manga "My Brother's Husband", which I would highly recommend to anyone who likes adorableness. Unfortunately, the excellent "Mike's Gay Culture Lectures" segment I got that fact in were cut from the official English release (I read a scanlation before I got my hands on it), presumably on the assumption that readers in the more gay-friendly US and Canada would already know this stuff. :-(

So why does the term exist? Probably because the guys look kinda like bears. Or maybe it morphed from the term "beards", another term referencing hairy men at the time. As for why it refers to gay men, that would be because the term lriginated and gained popularity in gay cultural circles, and thus became associated specifically with gay men.

I hope that makes sense.

...to put it in the bluntest of terms, really big, hairy, manly men who are gay. There’s a bear pride flag, even. I believe they have their own sub community of the LGBT+ populace, but that’s not my area of expertise, so I can’t really say much beyond that.

Smaller, hairy guys are called otters, in the same vein.