The universe of Legend of the Galactic Heroes is a large and complicated one. From the first few episodes, it is difficult to get a handle on what the show is really about and where it is going. In fact, part of the fun of the show is how broad it is, with deep characters, complex political maneuverings, clever military intrigues, and personal dramas. Telling too much of the nature of the story to come would ruin the enjoyment of watching a wonderful and detailed story unfold week after week, but some background can be provided to make each weeks' episode more meaningful to the viewer.
As you already know, the Galactic Empire and the Free Planets Alliance have been embroiled in a bitter war for over 100 years. It is the year 795 UC (Universal Calendar), equivalent to the year 3595 AD. Seven hundred and ninety five years ago, the United Space Government was founded, unifying all of human-occupied space under a single banner. For the next 310 years, a period of relative peace passed by until the rise of Rudolf von Goldenbaum. Originally a USG soldier of humble breeding, Rudolf was possessed of a unique charisma and military aptitude. In the year 310 UC, Rudolf overthrew the USG and restarted the calendar at the year 1 RC (Reich Calendar), and the Galactic Empire was born.
Rudolf and his successors ruled as iron-fisted emperors, but in the year 164 RC, a man named Ale Heinessen and thousands of his rebel cohorts secretly escaped from Imperial space on a long 10,000 light-year journey to a part of space where they felt would be difficult for the Imperials to follow. They landed on a planet across a region of unnavigable space and there founded the Free Planets Alliance and reinstated the Universal Calendar.
As time passed, the FPA grew stronger, strong enough to rival the Empire. At the same time, the Empire became more liberal in its policies while the FPA began to drift away from its founding democratic ideals. However, they still had no contact with each other until the year 331 RC (640 UC), when the Empire and the FPA met by chance in the Dagon star zone. Thus began the war which continues to rage on between to two governments.
The Empire considers the FPA to be a rebel group and seeks to return them to the control of the Empire. On the other hand, the FPA seeks to end Imperial aggression by ending their ability to wage war, and "free" the Imperial-controlled planets in the process. In reality, those in power on both sides of the war have lost sight and interest in the ideals behind the fighting, and now use the war to maintain their own personal political power. Both militaries are filled with incompetents, and both governments have grown more corrupt. (And that's all I'm going to say about the subject. To learn more, you must watch more.)
Now, a little geography; take a look at the map that accompanies this article. Between the Empire and the FPA is a region of unnavigable space which can be crossed only by following one of two corridors (a path of stars in which all ships wishing to cross the region must follow). The first is the Phezzan corridor, with the planet Phezzan in the middle.
While technically an Imperial province, the Phezzan have received special autonomy from the Empire in order to facilitate trade between the FPA and the Empire. Despite being enemies, there are many goods that people on both sides want from each other, and the Phezzan allow them to trade despite being enemies. The Phezzan greatly enjoy their position and have their own agenda which will be seen later.
The other corridor is the Iserlohn corridor, the most militarily important point in space. Since the Phezzan corridor is not usable for military operations because of their "special" arrangements, the Iserlohn corridor is the only way to get from one side to the other. Whoever can hold this point has a tremendous military advantage, and currently, the Empire has a doubly-tremendous control over the corridor, as will be seen.
This should be enough information to get yourself grounded in the series, but if you are really hungry for more information, point your web browser to http://www.nwlink.com/~logh/logh.htm.
Be warned though, don't deprive yourself of the pacing and the storytelling of this show by reading too much about the future of the show. Keep watching, and don't forget those names. They write them on-screen for a reason...