Nasically the Silmarillion is about
Illivatar made the world (Arda) with the humans and the elves. the rest of the ainur helped make earth itself and the other creatures
Melkor rebelled and was allowed to go down to Arda.... he is the one who leads to Sauron from LOTR
the Elves were granted special favour by the ainur, and some were allowed to live with them... this is why they sail across the sea in LOTR... they go to a .. kinda like a holy place
there was a war... the last alliance talked about in LOTR. They fought Sauron
in the middle of all of this people were trying to get hold of the Silmarils. Gems that were in the treees holding the great lanterns of the night and the day
one of these silmarils is the green stone in Aragorns crown...
He is heir of Isildur and the crown, and as he was brought up by the elves, he is loved by the gods, so he lived long (in addition to Arwen giving him of her long life)
..uhm yea, I think those are the basics