If we registered all of this information, we'd constantly be on mental overload. Again, think about sensory information. Have you ever had the experience of entering a room and noticing a bad smell, but then after a little while not being able to smell it anymore? When sensory information isn't changing, our brain decides that we don't really need continued awareness of it, and begins to filter it out. That's why they make those air fresheners called "noticeables," which alternate between two scents so that you can still smell them!
We don't have to think about filtering out information in this way - our brain just does it. That's usually good (since the point is to lessen our sense of mental overload), but it's also kind of scary: your brain is deciding what information to give you, and what not to give you, without your conscious participation. If it can filter out one of your five senses, what else is it filtering out?
Quite a lot, as it turns out. In fact, the mental filter is one of the more problematic cognitive distortions. The cliche "you see what you want to see" is actually not far off. It may be more accurate to say "you see what you expect to see." What happens is that our brains register our expectations, and then, as they're screening incoming information, screen in information consistent with our expectations, and screen out contradictory information. If your expectations are realistic, this is useful; however, if they are distorted (for example, by a belief in your own lack of worth, or the world being out to get you), competing information would be helpful.
Unfortunately, the brain is more geared to problem solving than anything else, so it tends to look for potential problems. Therefore negative information seems more likely to be screened in than positive information - further contributing to pessimistic expectations, assumptions, and behavior. Denial may be an exception - when it would be too painful to acknowledge something, our brains screen out confirming evidence, often resulting in a more positive view than is warranted. The end result is the same, however: behavior that does not take the complete picture into account, and therefore may not be fully adaptive to reality.
How else do you see the mental filter operating?