The confirmation bias is the tendency to cherry pick data to fit a hypothesis, avoiding any data which disproves that hypothesis.
Selective information gathering can apply either to selective memory or to selection of new data. A famous example of both is the lunar effect. Even the most level-headed emergency workers firmly believe that a full moon is associated with an increase in crime, emergency room admissions, and general weirdness. They remember how busy it was that night, and all the strange cases they encountered. When recollecting on their own, without guiding questions, they are unlikely to remember whether it was just as busy the previous Saturday.
When the same data is collected blindly, no correlation between these kinds of events and the phase of the moon has yet been found (Iosif and Ballon, 2005). However, by believing in the lunar effect, people pay more attention to confirming events which happen under a full moon, and much less attention to similar events which don’t support that belief. They also recall confirming evidence much more easily than contradictory evidence.
Just changing a single word in the question can be enough to elicit the confirmation bias. If a person is told to look for reasons in favor of an action, he will seek out and remember different information than if he is told to look for reasons against the same action, even when the objective data is identical in both cases.
For these reasons, a person who is unaware of the confirmation bias will constantly reinforce his own beliefs. This may result in an overconfidence unwarranted by an objective assessment of the facts.
Further information:
Why our brains do not intuitively grasp probabilities
Confirmation bias: an ubiquitous phenomenon in many guises
