Yes, now that it's kind of confirmed, I can say that Sasuke is trying to kill his brother Itachi, and Itachi murdered his entire clan, or took part in that process. Of course more will be revealed about it as the show continues.
This might be bit of a spoiler about Orochimaru, because I don't remember if it's mentioned until later, and I at least didn't really realize this until much later. But it can help you understand some things.
************************************
I only realized it in Shippuuden, when they talked about what techniques he had developed during his life. But Orochimaru at this current time, is one of the most powerful ninjutsu users in the entire world. He's mostly just playing with his "food" here. If Orochimaru wanted to kill them, Naruto and Sasuke would have no chance of winning against him. Just puts it into perspective, when you'll see one fight later on.
************************************