Nihil obstat is an official approval, certifying that a work dealing with faith or morals does not contradict Catholic teaching. The "Censor Librorum" reviews the work as delegated by a bishop of the Roman Catholic Church. The nihil obstat is not a certification that the reviewer agrees with positions or approaches in the work.
Translated into English, this Latin phrase means "nothing hinders" or "nothing stands in the way."
The nihil obstat, is the first step, along with the Imprimi potest, toward the granting of an Imprimatur. Under older Canon Law, a book written by a member of a religious order had to receive two nihil obstats by members of the order to receive the imprimi potest.