After the excellent "Game of Thrones" season 7 premiere, "GOT" fans are discussing all kinds of theories. Since plenty of them still wonder why Jaqen H'ghar was in Westeros, here you are the best possible explanation of the Faceless Man's presence in the Seven Kingdoms.
Alt Shift X's video
The brilliant Youtuber Alt Shift X provided a great deal of information about this mystery.
After reading the "Forsaken" chapter from George R.R. Martin's "The Winds of Winter," he finally understood why Jaqen was in Westeros when Arya first met him. He was there because he was sent to kill Balon Greyjoy.
The theory (spoilers on the "Forsaken" chapter from "TWOW" ahead)
In one of the "The Winds of Winter"'s chapter released by George R.R. Martin on his official site, Euron Greyjoy tells Aeron that he wasn't the one who threw Balon Greyjoy down the bridge. But admits that he was the one who ordered the assassination.
Well, in "A Storm of Swords" we can find a huge clue about who Balon's killer was.
The Ghost of High Heart (an old witch) speaks of the death of Balon in wording that suggests the Lord is assassinated by a Faceless Man. "I dreamt of a man without a face," says the witch, "waiting on a bridge that swayed and swung. On his shoulder perched a drowned crow with seaweed hanging from his wings."
The "man without a face" is obviously Jaqen H'ghar, and the crow on his shoulder is a reference to Euron Crow's Eye, who ordered the murder.
A faceless man costs a lot of money
We are told, in the show as well as in the books, that hiring a Faceless Man is very expensive. Paying for the assassination of such an important lord would probably cost a fortune. But this is not a problem for Euron "Crow's Eye" Greyjoy.
In the books, we are told many times of Euron's travels across the world. We are also told that he was able to obtain several priceless items from Valyria. Euron himself states that he found a dragon egg once, an egg which wouldn't hatch. According to Euron, he threw the egg into the sea; according to many fans, he might not have tossed away such a valuable item. He might have used it to pay for Balon's murder.
Beyond the dragon egg's story, we know for sure Euron owns a fortune. He owns Dragonbinder; he also owns (as we can see in the "Forsaken" chapter from Martin's "upcoming" book) an incredible suite of Valyrian steel armor. All things considered, we think this theory is very solid.
What about the TV series?
In the TV series, Balon Greyjoy, the head of House Greyjoy and Lord of the Iron Islands, is wounded and threw off a bridge by Euron. Jaqen is not the one who kills Balon in the show.
There are important differences between the show and the books. Considering only the show and not the novels, we can't say why Jaqen was in Westeros at the beginning of the story. We can speculate that the showrunners have cut out this sub plot to simplify the storyline, and since the show is coming to an end, we think that Jaqen's presence in the Seven Kingdoms will never be properly explained in the TV series.
Don't forget: the second episode of "Game of Thrones" Season 7, titled "Stormborn," will air on Sunday, July 23, on HBO.