Just from browsing around fandom, you will probably gather that there are two opinions on threesomes. The first is that they are a magical, mystical tool to solve all pairing wars and squish together any characters and pairings that seem kind of hot. The second is that they are an obnoxious, wishy-washy, unrealistic cheat to avoid taking a stand and making a choice of pairings. Guess what! I don't subscribe to either opinion. And that is why I must write this (and by "must," I mean, "feel the irrepressible urge to despite having better things to do").
I am an OT3 fan. I define this to mean that I enjoy relationships that a) involve three different characters and b) have some romantic or sexual element. Here are some ways I do not define it:
1) Liking every combination of three characters ever. There are OT3s that I do not care for. Even popular ones! Even "obvious" ones! I am not a Kyou/Tohru/Yuki fan, for example; if I have to pick a threesome in Fruits Basket, it's Yuki/Haru/Rin.
2) Wanting all of the OT3s I ship to jump into bed and have kinky threesome sex. I like Kaylee/Simon/River in Firefly as a three-person relationship with romantic/sexual elements to it, but I can't see Simon and River ever willingly having sex. I just think there's a slightly strange, arguably romantic angle to their sibling relationship that creates a particularly engaging dynamic when you throw Kaylee, her romantic/sexual relationship with Simon, and her (potentially romantic) friendship with River into the mix.
3) Shipping two pairings that happen to involve the same character. To go back to the Fruits Basket example: I do not ship Yuki/Haru/Rin because I like both Yuki/Haru and Yuki/Rin (in fact, I'm not a particularly big fan of Yuki/Haru on its own). I ship it because I think the dynamic the three of them had together as children was interesting and could turn into something more romantic now that they're grown up (although I prefer Yuki/Machi, to be honest, but that's another story). On the other hand, I do ship both Yoruichi/Soi Fong and Yoruichi/Urahara in Bleach (or did, when I was into it; whatever). But I hate the threesome that combines the two pairings. It does not form a three-person dynamic that I like.
4) Possessing the mystical solution to pairing wars. Shut up. Don't even. You're making people who actually like OT3s for what they are look bad.
So to me, an OT3 isn't an orgy or a combination of two pairings, any more than a pairing is just two characters having sex or standing next to each other. It's an at least partially romantic relationship structure built out of three people, the connections they have with each other, and the dynamic they possess as a group. An OT4 is the same, except built out of four people--and yeah, I have OT4s too, but they're more likely to have a strong, balanced familial aspect in place of or alongside the romantic aspect.
In comments to this post: explain what "OT3" means to you, or ask me what I think of a particular threesome, or whatever. Give me something more to tl;dr about!