The Five Star Stories is, to put it simply, a masterpiece. Everything about this series is done with such an eye for detail and a love of the craft that one can fall in love with it without even knowing what's going on. Despite that, let's have a brief summary.
The series takes place in the distant Joker Constellation. Joker was once home to an advanced spacefaring race, but it was destroyed by conflict. Now, the people of Joker look to the Headdliners, humans born with supernatural speed and reflexes, to fight their wars. Their main tools are the Mortar Headds, humongous mecha. But Headdliners cannot accomplish this feat alone: they require the assistance of a Fatima, an artificial human with enhanced mental abilities and uncanny beauty. Our story begins with Ladios Sopp, a Mortar Headd mechanic and designer who is actually Amaterasu-no-Mikado, God Emperor of the planet Delta Belune. Years ago, Ladios developed a bond with the young Fatima Lachesis. Now, he plans to make her his. But there are complications...
Over the course of 12 volumes, Mamoru Nagano accomplishes near-Tolkienian feats of world-building. All of Joker's history and culture is explained in depth, either in the main story or in various footnotes or extra pages at the end of each volume. Most of the story is told anachronically. Story arcs may be thousands of years apart, and some seem to have nothing to do with the main story until one looks at the timeline. This may be strange to newcomers, but it allows Nagano to have a lot of freedom in what he expresses.
If you can get hold of the Five Star Stories manga, read it. You won't be disappointed. If you can't, watch the anime: it only shows a small fraction of the story, but it allows one to get a feel for the setting and characters.
To sum up, Five Star Stories may be the 'Holy Grail' of manga. Every mecha fan should read it at some point in their lives.