The state of advaita is proclaimed to be the ultimate state to be. Why ? advaita translates to non-duality. That is a state in which the soul (pashu) does not feel any different from the Supreme (pati).
In the world the fear is the major component that affects the human life. An insect is threatened by a frog. The frog is worried about the snake. The snake gets frightened by the human hunters. The hunters are worried about their livelihood ! The same way a worker is worried about pleasing the manager and the owner about the government and market and the head of government about retaining the post ! This is a vicious circle.
One of the other thing could be the hunt for fame. One feels that he/she should command the respect of others in some way or the other. When that is achieved the person find out that there are taller mountains beyond the cliff already reached to pursue ! Keep getting promoted and promoted step by step - to end where ?
There could be many others one could imagine - the pursuit of better things. The ultimate thing to look for would be - to be the one that is ultimate ! The one that is does not have any superior element that could bully, the one that does not have external dependency to be happy, the one beyond which there can be nothing higher ! If we become that one, that is where going to be the point of completion. It is the Supreme Almighty ever Blissful - the One that qualifies for that ultimate thing. Being the favored of that Being would eliminate the fear and worry of everything else as the favor of the Almighty is there. Still isn't that one short ? There is still One Being to look up to and due to the fact that It is superior there is a fear, though with respect, for It. If the self unifies in that Supreme without recognizing itself to be anything other than the Supreme, the result would be just bliss - no strings attached ! This is the state of non-duality advaita.
The word advaita is used in this article more widely. (The upaniShat proclaim aham brahmAsmi). Not necessarily in the context of the advaita popularized by shankara bhagavatpAda.