Look at it this way... try to repeat each episode at least one more time if you don't understand it... it's bound to clear things up a bit at least...
But in totaity, there's nothing not to understand...
click to show spoiler
There is this high school student who got a notebook that when whoever's name is written on it will die in a matter of seconds of a heart attack otherwise specified.
He wishes to gt rid of criminals with it and create a new world where he is god.
However, he has encountered some obstacles aong the way.
That including his Father, a Mysterious guy named L, and two other people at the farther part of the story:
click to show spoiler
When L dies...
We get M and N
Mello and Near
and another unexpected thing occurs:
click to show spoiler
Mello dies
Near apprehends Light
Light dies because ryuk wrote Light's name down his Death Note
end of story
of course the additional stories are great in weaving the entire story... it shows how great the minds of the 3 people in the story are. Light, L, and the other person as stated in the 3rd spoiler (second spoiler in the spoiler).
That's it... sorry if i summarized the story too much... But watch the whole thing... It's really really great!