: : Well, Tolkien intended this to be part of the great tragedy of the Elves. They were immortal but fated to fade as Men rose to the ascendant. They are preserved and made whole again in Aman, the Blessed Realm.

: Persia: what is Aman the Blessed Realm is that like the Elvish heavan or something?

Yes and no. Yes, it was a sort of paradise for elves where there was peace, no disease or evil and they lived forever without fading or dwindling. On the other hand it was unlike heaven because Elves didn't have to die to go there, but could also get there by sailing West across the sea (and presumably return, although there is no evidence of any doing this). Originally, it was a geographic place anybody could get to, guarded only by high mountains and the Vala themselves, but later (at the time of the destruction of Numenor) it was magically asundered so that only the ships who the Vala wanted to get there would actually find it.

This is only a very very brief summary of all the things Aman is and what happened there and why. You could find out more in the Silmarillion.