It's hard to describe.

A common misconception is that moe (pronounced not like the name "Moe" but more like "moh eh") is a description of something, like how the word "cute" describes a certain way that something looks. Instead, moe is a feeling you experience, and you say that something "is moe" if looking at it makes you feel the "moe" feeling. You also say that someone "has a moe for" something if it's something that often/usually makes that person feel moe. I don't think moe is a "strange" feeling, I think it's something most people experience but they just don't describe it in this way.

Another common misconception is that moe is sexual in any way, but it emphatically is not. That doesn't mean moe can't coincide with sexual feelings, but more often than not it doesn't. Actually, I might partly describe "having a moe for something" as a nonsexual fetish.

A commonly cited etymology is the Japanese word "moeru", meaning to burn up (though I don't know how accurate that is). Moe is an intense feeling of passion for something, often said to involve a desire to "protect". This doesn't necessarily mean "protect from harm"; often it's much more like "I don't want this thing to ever disappear".

Another misconception is that "thinking something is moe" means "it's cute". Moe doesn't necessarily have anything to do with cuteness. As an example, someone could have an intense moe for glasses characters, meaning essentially they really love characters with glasses regardless of anything else like how cute they are. I think this cuteness misconception comes from the proliferation of a certain type of anime around the late 2000's/early 2010's, focusing mostly cute girls not doing much else than being cute. These shows were certainly intended to make their audience feel moe, and the word was applied a lot to describe them, and so people unfamiliar with the word naturally though "moe" described these shows specifically.

Moe is often associated with anime/manga/etc. and you could reasonably restrict it to apply only to this sphere by definition, but I don't think this is necessary. But because of that it usually designates a space as anime-related.

So these "X-moe" communities are communities for sharing images that someone who has a moe for X would enjoy, and also implicitly these are "anime-esque" images because "moe" as a word sort of codes for those sorts of communities.