Credibility is defined as "the quality or power of inspiring belief". Credible sources, therefore, must be reliable sources that provide information that one can believe to be true.
It is important to use credible sources in an academic research paper because your audience will expect you to have backed up your assertions with credible evidence. Think of it this way: if you went to the doctor to get advice on a symptom you were having, and your doctor told you his diagnosis was based on something he heard a random stranger say on his way to work, would you be inclined to trust what he told you your symptom meant? Probably not. But, if your doctor told you his diagnosis came from an article he read in the peer-reviewed, highly prestigious Journal of the American Medical Association, you would be more likely to believe his diagnosis was correct. Why? The reason is that you may have heard of the journal your doctor referred to, or you may know that the AMA is a highly respected organization in the field of medicine, ergo, they know that their information is credible and reliable. The same situation holds true if you are writing a research paper. Your audience is going to expect you to use the best, most correct, most recent, and most reliable information possible so that they can trust in your expertise. Using evidence that does not come from a credible source of information will not convince your reader that your claim is plausible or even correct.