The Catechism of the Catholic Church, citing Lumen Gentium 25, states the following:
892 Divine assistance is also given to the successors of the apostles, teaching in communion with the successor of Peter, and, in a particular way, to the bishop of Rome, pastor of the whole Church, when, without arriving at an infallible definition and without pronouncing in a “definitive manner,” they propose in the exercise of the ordinary Magisterium a teaching that leads to better understanding of Revelation in matters of faith and morals. To this ordinary teaching the faithful “are to adhere to it with religious assent” which, though distinct from the assent of faith, is nonetheless an extension of it.
The big problem with this is that nobody seems to have any idea just what “religious assent” means. The Encyclopedia Britannica online, under the entry for “religious assent,” even declares that it is “a term that is extremely difficult to define.” - britannica.com/bps/topic/497272/religious-assent#tab=active~checked%2Citems~checked%3E%2Fbps%2Ftopic%2F497272%2Freligious-assent&title=religious%20assent%20–%20Britannica%20Online%20Encyclopedia
This is a question that I’ve asked many times in many places, and which others have as well, including here. I’ve never seen a good answer. I spent several hours tonight reading all sorts of websites, articles, and even scanned pages of old theology books from as far back as 1935 regarding the issue. I can’t seem to get anything all that useful.
So I’m posting this in the hopes that somebody somewhere may just happen to have some source that provides a meaningful definition.
Now, from all I have read, whatever this religious assent happens to be, it is something that Catholics are bound to submit to interiorly and unequivocally. There is no room for questioning items held with religious assent. This brings me to a bit of a corollary:
If there exist items not infallibly defined, yet which no question is able to question, then how in fact are they really at all reformable? It seems that such teachings could, in fact, never really change, as they can never licitly be questioned.
Peace and God bless