Catholic teaching holds that the Church is indefectible. She can never fall away into error, but will forever hold fast to the true faith.
The teaching authority of the Catholic Church resides in the “Magisterium,” which is simply the body of bishops who govern the Church in communion with the Bishop of Rome, the Pope. God has given what I’ll call the “gift of reliability” to the teachers of the Church, so that what they teach in terms of the doctrine of the church (whether of “faith” or “morals”) is accurate and does not lead into error. This gift is not given to individual bishops acting alone, but only to the body of bishops as a whole–so it is possible that individual bishops, or even bishops in groups smaller than the whole of the body of bishops, might teach error, but the body of bishops as a whole can never do so. Also, the Pope, as the head of the Church, has the gift of reliability given to him in his own unique office as well, so that he can never teach error when he is exercising his teaching office.
Sometimes the Church teaches a doctrine definitively–that is, she teaches a doctrine as certainly and irrevocably the correct opinion. This might happen when the bishops come together in an ecumenical council and make definitive decrees or statements, or it might happen as all the bishops in the ordinary exercise of their office agree in teaching a doctrine definitively throughout the world. The Pope might teach a doctrine definitively either by formally defining a doctrine (this is the famed ex cathedra declaration) or simply by affirming that a doctrine is the definitive teaching of the Church. When the Church teaches something definitively, since she has the gift of reliability, Catholics are obligated to receive and accept it definitively. Sometimes, however, the Church might teach a doctrine non-definitively–that is, she might teach a doctrine in such a way that it is claimed to be true, or accurate, or good to believe or hold or practice, etc., but not in such a way that it is claimed that the final, unchangeable word on the subject has been given. The doctrine is not claimed as definitely certain or true or unchangeable in its current form. For example, the bishops or the Pope might say, “X is the best way to think about this right now,” or “We should think X right now,” or “So far as we can see at this point, X appears to be true,” or “We should do things in this way right now,” etc. There could be lots of ways such a non-definitive teaching could be given and a variety of degrees of certainty in such pronouncements–context would determine how to interpret any particular statement or teaching. A non-definitive teaching must be accepted and adhered to by Catholics as well. It must be accepted in the way and to the degree it was intended by the Church–again, interpreted by context.
A little more on the distinction between definitive and non-definitive teaching:
The teaching of the Catholic Church is that the Pope, and the bishops as a whole, can teach with various levels of definitiveness, but that Catholics are bound to submit with mind and will to all magisterial teaching according to the intention of the magisterial teacher. So if the Pope teaches something and intends it to be a definitive pronouncement, Catholics are to submit to it as the final word on the subject and irreformably and forever true. If the Pope teaches something which he intends the people to believe, but it is not intended as necessarily the final word on the subject, then Catholics are bound to accept that teaching, but not necessarily as the final word on the subject. All magisterial teaching is to be regarded as inherently reliable, for it all comes with the authority of Christ and the guidance of the Holy Spirit. We can never be led astray by following magisterial teaching, although non-definitive teaching can lead us to provisional conclusions that may later turn out to be augmented or even corrected. The fact that non-definitive teaching is not necessarily irreformable is not contrary to its reliability, for the reformable nature of such teaching does not come from any unreliability in the teaching but in the non-definitiveness of the magisterial intention. If the Pope teaches us that X is the best position to hold right now and that we ought to hold position X, but that this is not necessarily the final word on the subject, if later on we find that X is false we cannot be said to have been led astray by the Pope’s teaching, for that teaching did not teach us that X would never be overturned. But the reliability of the Pope’s ordinary teaching obviously precludes that teaching from including ideas that contradict what the Church has previously affirmed definitively–so, for example, heresy cannot occur in papal teaching (or any magisterial teaching), since “heresy” involves the denial of previously definitively taught dogmas–for we already know that such teachings cannot be true and that we should not hold them. It would be contrary to the justice and truth of God for legitimate authority appointed by him to legitimately bind us to teaching that it would be wrong to hold.
With regard to definitively infallible teaching, the Code of Canon Law tells us that we are not to assume that any teaching of the Magisterium has been defined infallibly “unless this is manifestly evident” (Code of Canon Law #749.3).