Estel (philosophical concept)
In addition to its common meaning, the Elvish word estel (found in both Quenya and Sindarin) refers to a complex philosophical concept found in Elvish thought. This idea is best understood as trust or "faith", and the hope that comes from it: estel refers to the belief that Eru Ilúvatar, the Creator of the Universe (Eä), is good and that his designs for his creatures will ultimately be good as well, despite the troubles that seem to plague Arda, this world. Certain knowledge of what is to happen to the Elves after the end of Arda has thus been withheld from them, so that all they can rely on is estel. The Elven-king Finrod Felagund explained estel as an idea that "is not defeated by the ways of the world, for it does not come from experience, but from our nature and first being. If we are indeed the Eruhin, the Children of the One, then He will not suffer Himself to be deprived of His own, not by any Enemy, not even by ourselves."
Estel is also connected to the more immediate hope found in the Children of Ilúvatar that keeps them from being overcome by the hardships of Arda Marred; the Valar refer to this gift as the ability to see "the Unmarred that they discern in the Marred". That is, the Children of Ilúvatar can see what is good about Arda Marred, despite its corruption by Morgoth. It is estel that gives them this ability.
Estel is similar to, but more deeply based in the heart than, amdir, another Sindarin word that can be translated as "hope".
Estel in Arda's History
According to Elvish tradition, estel was one of only two things Eru demanded from his Children; the other was belief that he existed in the first place. Lack of estel was seen as a fault in the fëa of a person, and could have grave consequences: the most drastic example of a being lacking in estel is none other than that of Morgoth himself; his denial of the greatness of Eru led to his nihilism and despair. The failing of estel found in Finwë, the first High King of the Noldor, of his wife Míriel ever returning to him from the Halls of Mandos is another example. Finwë's decision to take another wife led to the strife between his sons that was instrumental to the tragic Fall of the Noldor. Ultimately, most poor choices of Elves and Men come from a failing in estel.
Estel and Men
Unlike the Elves, the foundation of estel in Men was shaken because of their corruption by Morgoth in the earliest days of their race (one version of the story of their Fall is found in the Tale of Adanel). Because they had denied the supremacy of Eru and taken Melkor as their God, they could no longer believe with certainty that Eru would accept them. This lack of estel in Men had an effect on their view of their mortality, which was originally their Gift from Eru.