The Latin phrase nihil obstat ('Nothing stands in the way, obstructs, or prevents') is used in English as a noun. A nihil obstat is a statement or declaration to the effect that there is no (official) objection to a proposed course of action such as an appointment to a position or the adoption of a new policy - for example, 'We have had a nihil obstat from the Vice-chancellor to the appointment of another professor in the Chemistry Department'.
The phrase 'nihil obstat' was originally, and is still, used within the Roman Catholic Church. When the approval of the Church is sought for the publication of a document (e.g., a book or pamphlet), the bishop appoints a censor whose task is to determine whether the document contains any material 'offensive to faith or morals'. If on examination the censor concludes that the document does not contain any 'offensive' material, he informs the bishop of this by issuing a nihil obstat (i.e., 'Nothing stands in the way (of publication')), and the bishop then (usually) gives his permission for the document to be published with the Church's approval by issuing an imprimatur (i.e., 'Let it be printed').
See further Imprimatur.