Quick Tolkien Geography lesson: Middle-earth is a section of the world known as Arda. We only see bits and pieces of Middle-earth throughout The Fellowship, but we know enough about it that we can tell it's chock-full of all the elements a fantasy world needs to become truly fantastic.
Unfortunately, at the time of the LotR, Middle-earth ain't doing so well. The dwarves, usually so hardy in their mountain halls, have suffered great losses at the hands of the goblins. The elves are leaving, heading back to their homeland in the west. This is the age of men… and men are highly irresponsible and greedy.
All this is going down in the third millennium of the Third Age. The War of the Last Alliance (the one with Elendil and Isildur and the finger cutting) marks the end of the Second Age, which lasted close to 3,500 years. That means that 3,000 years have passed between that war and the current story… the ending of which will mark the end of the Third Age.