Some context for the Newtype and Zeon stuff (also
spoilers), since Unicorn isn't really going to make sense without it: UC Gundam was written in the late 70s and 80s, right around the time psychics were popular in science fiction. That's what Newtypes are, space opera psychics.
Since Newtypes have literal telepathy (that can work unconsciously), they get together and start wanting to bone pretty quickly. It's anime as fuck, but it kind of makes sense since telepathy is OP.
A guy who founded a space colony country called "Zeon" decided "Hey, Newtypes are a pretty dope idea for making everybody friends and ending war.", and then he was killed because politics. A guy called Degwin Zabi (Space Hitler) took over Zeon and turned it into Space Nazi Germany, and threw a giant space colony onto Sydney as a declaration of independence from the Earth Federation. Also they had a really cool guy called Char Aznable
Then they figured out Newtypes were pretty OP for mecha, since you could stick a bunch of psychic receivers ("psycommu", a name that sounds like crap in English) onto one and have a Newtype control it with their mind, Pacific Rim-style ("psycoframe", also sounds pretty bad). Plus, the Minovsky reactors used in space and mobile suits break wireless communication, but don't do shit to psychic signals, so your mecha can now fire guns that shoot lasers!
Oh and they invented a way to make Newtypes artificially and then called them "Cyber-Newtypes", which probably sounded better 30 years ago.
After the original series and Zeta Gundam, Zeon blew up, and the guys who were left behind formed Neo Zeon. Think Galactic Empire -> First Order, and you get the idea. Then they
also blew up,
. And then a
third Neo Zeon popped up, led by a guy called Full Frontal, and they got nicknamed "the Sleeves" for reasons. They're basically Space Al-Qaeda. And that's where Unicorn starts.