There are those who talk about the intellectual state of being "pre-critical." Without trying to oversimplify things, someone who is in the pre-critical stage in their thinking tends to accept things at face value based on the recommendation of a respected authority, family member, etc. They have not asked the hard questions or entertained contrary ideas and, in fact, may not even be aware of opposing ideas. The term a priori is reserved for the knid of knowledge received and accepted without question or investigation; knowledge that is assumed to be true.
Critical reflection is a particular way of approaching information which investigates all claims, accepting those that bear up under scrutiny, and rejecting or tabling those that don't.
An example of critical reflection could be the following: you read a book written by someone claiming to actually believe in Santa Clause. You throw out that claim, dismissing it as untenable and preposterous. However, in the book, the person makes the case that Vitamin C will boost your immune system. After investigation, you find corroberating evidence from experts who all support the claim, so, you decide to retain that knowledge, but you remain unconvinced about Old Saint Nick.
Now, sometimes people will throw the baby out with the bath water, deciding that an adult who believes in the existence of Santa Clause couldn't possibly have anything to teach us about other things. But critical reflection allows you to keep the knowledge that is good and dispense with the information that is false, etc. It is about the knowledge itself more than about the teacher (although knowing the teacher helps when processig the knowledge, and, frequently, if the teacher is off, so is the knowledge. But, with critical reflection, I do not have to make those assumptions, but can, rather, take the knowledge piece by piece. Later, if necessary, I can formulate an assessment of the teacher.)
It is a dangerous thing to give rise to critical thinking if you are not prepared for it. It can cause you to question bedrock principles and truths that are valid but not "provable" by scientific method, such as Christian faith. It can bring you into contact with those who clearly do not have faith but only questions.
For example, a Christian who has not been exposed to much background information about the greek New Testament and the process of textual transmission, etc., may consider it blasphemous that the New International Version of the Bible does not include the word fasting in Mark 9:29. I understand that the reason for the exclusion is that the oldest manuscripts don't include it, which is an arguement that perhaps the word was added to the text at a later date, which experts call a gloss. My faith is not shaken, nor do I fear that fasting as a spiritual practice has been threatened, because I know that Scripture is clear in many other places concerning the importance and power of fasting. So, whether I agree or disagree with the editors of the NIV, I can navigate my way through an issue that could otherwise potentially assault my faith or discourage me.
What does knowledge of critical reflection do for me? Well, it helps me to keep things in proper perspective when I might be tempted, as Robert Frost said, "to carry praise or blame too far." That is, it helps me to retain balance when dealing with people, not going too far to elevate or villify those around me.
For example, I was thinking how thankful I am for the Fox News Network and their fearless display of Scripture and Christian values during the holiday season. They actually take that approach all year long. Now, I am not foolish enough to assume that everyone at Fox is a practicing Christian. But I can be thankful that, in these times when Christian and American values are under such attack, there are those who are using their influence to promote them.
Finally, we cannot completely separate ourselves from facing the truth about the character of those around us, but we can learn from almost anyone, even when they differ from us on important issues. Critical reflection allows me to throw out the bath water and keep the baby.