It has been a while since I studied it at school, but I'll tell you what remains in my imperfect memory.
The Tale of Heike details the events of the Gempei War, which marks the delination from the end of the
Heian Period (794~1192) and the beginning of the
Kamakura Period (1192~1333).
A little more specifically, it describes the clash between two powerful families or clans, the Taira and the Minamoto clans. The Taira was a powerful family in the government, and the
Minamoto clan originated from the imperial family.
In the end, the Minamoto Clan wins and establishes the Kamakura government.
I remember being told that the Tale of Heike was written to appease the spirits of the
Taira clan, who lost. The epic has other stories interwoven into the tale, and it comes from a Buddhist perspective. Namely, the concept of "nothing lasts forever" and the idea of "cause and effect".
I'm sure you could get much better information than this by doing a simple web search, though! That's all of the coherent information that I can remember from the top of my head.