Jaqen H’ghar is certainly a Faceless Man of Braavos, the most mysterious and costliest of assassins (I: 297). Whether Jaqen is merely another of his many guises or his true identity is an open question. Given the speculation that a Faceless Man assassinated Balon Greyjoy (see Prophecies), it is tempting to believe that Jaqen himself carried out this deed. However, given his appearance in Oldtown at the start of A Feast for Crows, the timeline may make this prohibitvely unlikely (see 6.2.9. Who is the alchemist in Oldtown?).
Why he was in the black cells is an open mystery. It seems unlikely that this was all part of his plan, so it seems likely that something went wrong. One possibility is that he was in fact Syrio, who rather than being killed was imprisoned (see 6.1.3. Is Syrio Dead?).