Nestorianism was one of the early Christological debates, arguments about the nature of Jesus Christ. Nestorius was, oddly enough, the Patriarch of Constantinople for a while.... his argument ran along the lines of Christ being a man who was possessed by the holy spirit, rather than the official doctrine that he was one being which had simultaneous divine and human natures. He was condemnded at the Council of Ephesus in the 430s or so. Compared to Arianism or Monophysitism, Nestorianism was kind of an 'also-ran' as far as christian theology goes. Other than doctrine like that, it doesn't seem to have been _that_ different from other strains of early christianity, to judge from what few things are left about them, though less tied up in the church hierarchies and so on. You might be able to make a case for a slightly more overt Zoroastrian influence, seeing as lots of Nestorians were to be found in the Sassanid lands.... making general statements is almost impossible, though, since Nestorian communities out to the East tended to be small, very widely-scattered, and pretty autochthonous.