According to Catholicism, what is an imprimatur? What is the scope of an imprimatur? What does a work having an imprimatur mean for that work? What does it mean for the body of doctrine itself?
Imprimatur and Nihil Obstat

"Imprimatur" is Latin for "let it be printed."  An imprimatur is a bishop's permission to print a religious book.  The bishop is always the local ordinary of the author who wrote the book.  The Catholic Code of Canon Law, canons 822-4, requires pastors to help guide the faithful in their use of social communication and particularly books.  The imprimatur is one way that charge is carried out.

An imprimatur is always preceded by a "nihil obstat," which is Latin for "nothing stands in the way."  This is the judgment that the religious book contains no significant doctrinal errors.  Both the imprimatur and the nihil obstat are negative judgments insofar as they are not meant to positively approve the contents of the book, but are merely meant to say that it is not disapproved.  It sometimes happens that imprimaturs or nihil obstats are revoked after a period of time due to a discovery of doctrinal errors in the work.



Answering Specific Questions


"What is the scope of an imprimatur?


The scope covers the entire book as published, but not new versions of the same book.  It is a practice which is only carried out for religious texts because it is a judgment about how the book comports with the doctrines of the Catholic Church, doctrines which involve faith and morals.  It is a negative assessment insofar as it is not meant to approve the book or any proposition in the book.  It is not an endorsement (see above).


"What does a work having an imprimatur mean for that work?"


It means that the local bishop believes the work is fit to print.  See above for more detail.


"What does it mean for the body of doctrine itself?"


As far as the deposit of faith of the Church is concerned, it means very little.  Per canons 822-3, it is a service to the faithful, not a means of developing or promulgating doctrine.  Although it is a judgment about the presence of errors in a work, imprimaturs and nihil obstats can be revoked, as noted above.  It is also a diocesan-based initiative in the sense that each diocese has a bishop and at least one censor (a theologian approved to render a nihil obstat), so the opinion represents the decision of a single diocese rather than the whole Church.



Newman on St. Alphonsus Liguori

St. John Henry Newman writes about the beatification process of St. Alphonsus Liguori, part of which was an examination of Liguori's writings in a way that would be very similar to the examination carried out by those authorized to give the imprimatur or nihil obstat.  Although this process is more precise, thorough, and authoritative than an imprimatur or nihil obstat, I believe it may help shed some light on your question at a deeper level.  Please forgive the length:


  It is supposed by Protestants that, because St. Alfonso's writings have had such high commendation bestowed upon them by authority, therefore they have been invested with a quasi-infallibility. This has arisen in good measure from Protestants not knowing the force of theological terms. The words to which they refer are the authoritative decision that "nothing in his works has been found worthy of censure," "censurâ dignum;" but this does not lead to the conclusions which have been drawn from it. Those words occur in a legal document, and cannot be interpreted except in a legal sense. In the first place, the sentence is negative; nothing in St. Alfonso's writings is positively approved; and secondly it is not said that there are no faults in what he has written, but nothing which comes under the ecclesiastical censura, which is something very definite. To take and interpret them, in the way commonly adopted in England, is the same mistake, as if one were to take the word "apologia" in the English sense of apology, or "infant" in law to mean a little child.
  
  
  Now first as to the meaning of the form of words viewed as a proposition. When they were brought before the fitting authorities at
  Rome by the Archbishop of Besançon, the answer returned to him
  contained the condition that those words were to be interpreted, "with
  due regard to the mind of the Holy See concerning the approbation of
  writings of the servants of God, ad effectum Canonisationis." This is
  intended to prevent any Catholic taking the words about St. Alfonso's
  works in too large a sense. Before a saint is canonised, his works are
  examined and a judgment pronounced upon them. Pope Benedict XIV. says,
  "The end or scope of this judgment is, that it may appear, whether the
  doctrine of the servant of God, which he has brought out in his
  writings, is free from any soever theological censure." And he remarks
  in addition, "It never can be said that the doctrine of a servant of
  God is approved by the Holy See, but at most it can [only] be said
  that it is not disapproved (non reprobatam) in case that the revisers
  had reported that there is nothing found by them in his works, which
  is adverse to the decrees of Urban VIII., and that the judgment of the
  Revisers has been approved by the sacred Congregation, and confirmed
  by the Supreme Pontiff." The Decree of Urban VIII. here referred to
  is, "Let works be examined, whether they contain errors against faith
  or good morals (bonos mores), or any new doctrine, or a doctrine
  foreign and alien to the common sense and custom of the Church." The
  author from whom I quote this (M. Vandenbroeck, of the diocese of
  Malines) observes, "It is therefore clear, that the approbation of the
  works of the Holy Bishop touches not the truth of every proposition,
  adds nothing to them, nor even gives them by consequence a degree of
  intrinsic probability." He adds that it gives St. Alfonso's theology
  an extrinsic probability, from the fact that, in the judgment of the
  Holy See, no proposition deserves to receive a censure; but that "that
  probability will cease nevertheless in a particular case, for any one
  who should be convinced, whether by evident arguments, or by a decree
  of the Holy See, or otherwise, that the doctrine of the Saint deviates
  from the truth." He adds, "From the fact that the approbation of the
  works of St. Alfonso does not decide the truth of each proposition, it
  follows, as Benedict XIV. has remarked, that we may combat the
  doctrine which they contain; only, since a canonised saint is in
  question, who is honoured by a solemn culte in the Church, we ought
  not to speak except with respect, nor to attack his opinions except
  with temper and modesty."
  Then, as to the meaning of the word censura: Benedict XIV. enumerates a number of "Notes" which come under that name; he says,
  "Out of propositions which are to be noted with theological censure,
  some are heretical, some erroneous, some close upon error, some
  savouring of heresy," and so on; and each of these terms has its own
  definite meaning. Thus by "erroneous" is meant, according to Viva, a
  proposition which is not immediately opposed to a revealed
  proposition, but only to a theological conclusion drawn from premisses
  which are de fide; "savouring of heresy," when a proposition is
  opposed to a theological conclusion not evidently drawn from premisses
  which are de fide, but most probably and according to the common mode
  of theologising, and so with the rest. Therefore when it was said by
  the revisers of St. Alfonso's works that they were not "worthy of
  censure," it was only meant that they did not fall under these
  particular Notes.
  
  
  But the answer from Rome to the Archbishop of Besançon went further
  than this; it actually took pains to declare that any one who pleased
  might follow other theologians instead of St. Alfonso. After saying
  that no priest was to be interfered with who followed St. Alfonso in
  the Confessional, it added, "This is said, however, without on that
  account judging that they are reprehended who follow opinions handed
  down by other approved authors."
  
  And this too, I will observe, that St. Alfonso made many changes of
  opinion himself in the course of his writings; and it could not for an
  instant be supposed that we were bound to every one of his opinions,
  when he did not feel himself bound to them in his own person. And,
  what is more to the purpose still, there are opinions, or some
  opinion, of his which actually has been proscribed by the Church
  since, and cannot now be put forward or used. I do not pretend to be a
  well-read theologian myself, but I say this on the authority of a
  theological professor of Breda, quoted in the Mélanges Théol. for
  1850-1. He says: "It may happen, that, in the course of time, errors
  may be found in the works of St. Alfonso and be proscribed by the
  Church, a thing which in fact has already occurred."




Sources


Wikipedia - Imprimatur
Wikipedia - Nihil Obstat
"What are Imprimi Potest, Imprimatur and Nihil Obstat?" by Fr. Bartunek
Apologia pro Vita Sua, by John Henry Newman (Section 8 of the appendix)
Code of Canon Law, Canons 822-4