> You were now "the Chosen One" (in Daggerfall you were just a random person, except for being a friend of the emperor, living their life and trying to make fortune)
It should be noted that in Morrowind, that is very much ambiguous.
WARNING: MAJOR STORY SPOILERS!
The only thing that is really special about your character in Morrowind is that you're born "on a certain day to an uncertain parents", which technically makes you a viable candidate for the local prophesy about a reincarnation of a long-dead hero of the past. But, of course, plenty of people would also qualify based on something so vague.
From there, the Empire takes you - a prisoner - releases you, and drops you into Morrowind to work for its spy agency, on the basis that this background would allow you to infiltrate the local Houses. You also get a mysterious vision related to said prophecy, but there's a catch that becomes obvious later. Your spy handler then actively encourages you to perform actions that would be seen as fulfillment of various other conditions of that prophecy. At some point, the very goddess that issued that prophesy in the first place intervenes and takes over, and goads you further along the same track (this is especially ironic since she is, among other things, a goddess of fate and prophesy). She was also the source of that original vision that you had.
Of course, this invites the question: if you deliberately do things that the prophecy says a certain person will do, because you're forced by others to do so specifically for the sake of fulfilling it, does that really count? What if you're guided by the one who made the prophesy in the first place? Is it really fate?
This is a question that the game asks again and again. If you study the background of the prophesy (by e.g. reading in-game books), you quickly find out that there have been several people before you who were also candidates, and who have claimed to be a reincarnation, trying to fulfill the prophesy in various ways - and all of them have ultimately failed and died. It gets better still - in the second part of the main quest, you find a cave with the spirits of those past claimants, and they tell you their stories. Every one of them sincerely believed to be the reincarnation - and moreover, they also had visions telling them that they really are, just as you did at the beginning of the game.
To the very end, it remains an open question: are you really the reincarnation, and those others weren't? Or maybe all of you were, but you only stay one so long as you succeed? Or perhaps the whole thing is a lie, and the prophecy is no prophecy at all, and is "fulfilled" simply by forcing people to try to do it until someone finally succeeds? It's never really answered - right before the final boss battle, the Bad Guy (who slayed the original hero you're supposedly the reincarnation of) straight up asks you if you really are his old enemy. You can give various answers to that - including "I don't know" - but in the end, that's still just your character's opinion; there's no incontrovertible proof either way, other than you fulfilling the prophesy in terms of performing the actions you were supposed to. To everybody else, that is enough, and you're celebrated as the reincarnation. But is it enough for you?