The answer you are looking for can be found in Chapter Eighteen of this excellent novel. Be aware that through these two rival families Twain is satirising the nature of feuds and the concept of honour in the South. Note how Buck explains what a feud is to the curious Huck:
"Well," says Buck, "a feud is this way: A man has a quarrel with another man, and kills him; then that other man's brother kills him; then the other brothers, on both sides, goes fro one another; then the cousins chip in--and by and by everybody's killed off, and there ain't no more feud. But it's kind of slow, and takes a long time."
It is obvious that this hilarious response focuses on the ridiculous nature of feuds, as families slowly are eradicated as one by one members are killed and the remainder feel honour-bound to kill in response, triggering a never-ending cycle of violence and sadness. When Huck asks Buck what the original reason for this feud was, Buck admits that he does not know why such a longstanding feud exists between these two families. Thus Twain satirises such feuds, which are often maintained long after the original wrong was committed. Even though nobody can remember this original wrong, the reason for so much bloodshed, the Grangerfords and the Shepherdsons are shown to be more in love with the feud and violence than with any possibility of peace.