This show comes from a series of novels. The novels are divided into eras, the first era is the era we are living in now, then subsequent eras have humanity going out into space. The era in which Horizon In the Middle of Nowhere comes into play is called Genesis. In this era humanity could not stay in space because of war and had to come back to Earth. On earth the only place that habitable for human life was Japan. Naturally the Japanese wanted Japan so they got it. At this time they had the technology to build an extra dimension of space on top of Japan. All the other countries lived there. Now these people wanted to go back into space but they did not have the ability to do so, so they created a thing called the Testament. The Testament is essentially a self writing history book and the people in Japan and the people in the extra dimension were to follow it so that one day they would get back into space by repeating history they will get the know how. Somehow while the Japanese were repeating a civil war it got so out of hand that the mechanism that was holding up the extra dimension collapsed. So extra dimension collapsed on top of Japan that's why there are two moons, both parts are mixed together. So the kings of the other countries went to war against the Japanese and won. When this happened the Japanese became second class citizens in their own country. To further make it worse the kings joined forces with the Japanese daimyos and combined. So they recreate Japanese history and world history at the same time. One hundred something years later, Tori is at home tastes Horizon's food says that it tastes bad hurts Horizon's feelings, and she runs out. Horizon is so upset she keeps running, Tori runs after her she's so upset that she runs onto the road while a carriage passes by and it hits her and Tori, this while they are seven or eight I think. The person in the carriage is Horizon's dad, Motonobu Matsudaira (the guy with the graduation cap),he becomes upset. Tori becomes upset, and Horizon dies. In this world souls can be transferred on to objects. It seems Matsudaira transfered Horizon's soul on to a robot and 8 weapons. P-01s is Horizon's soul with her emotion of jealousy. The 8 weapons are armors of deadly sins, by a greek interpretation of the deadly sins I forgot the name I think I studied him in medieval history class in college, anyways. Matsudaira snuck Horizon on Musashi, Musashi is a ship on "Horizon in the Middle of Nowhere" but during Sengoku times Musashi was the province where present day Tokyo is, that's why some of the ship names are parts of Tokyo. Mikawa is a province to the south of Musashi. Since Tori thinks P-01s looks like Horizon, he wants to go out with her, I guess there is no bias with going out with androids. Before this could happen Matsudaira blows up Mikawa's ether generator, it's the energy that gives everyone their cool powers. He tells everyone that Horizon/P-01s is the ultimate operating system for the armor of deadly sins, but the only way to get to it is for Horizon to suicide. Horizon is a nice android and it seemed she didn't mind, except her guy Tori didn't want it to happen. Tori got his class to try and go after Horizon.

This is all well and good but there is a problem with the Testament it has been working to repeat history but it seams to have stopped at the year 1640, I think, after that nobody knows what will happen, so people think it's the apocalypse. Tori and his friends go and save Horizon, says he'll collect all the armors of deadly sin, and save the world from apocalypse, but by doing that he pretty much declared war on everyone.
That's pretty much the basics I know so far, from the first season. Second season so far is interesting and I will write my thoughts about it after the end of the season after I've watched it multiple times and read up on back story from various blogs and wikis.