Your brain lies to you. It does it all the time. It's for your own good, really, but you have a more accurate picture of the world if you take into account the fact that you can't really trust your own eyes.
Your senses take in huge amounts of data every second, way more than you could consciously deal with, but most of it gets thrown away. If I'm looking at my computer screen, many other things are in my field of view. I can see my keyboard, the wall, my mouse, the speakers, the brand logo on the bottom of the monitor...but I don't notice any of these. The light from them hits my eyes. My brain does just enough processing to determine that they aren't moving. It decides that they are uninteresting, and throws the information away.
Your brain is doing this sort of thing all the time, and is really pretty good at it. It's pretty rare that you're looking for something and not finding it, and it turns out you were looking right at it. I mean, it happens, but it's unusual when it does. Unusual enough to be remembered.
Which brings us to another area where most of the information gets thrown away: memory. You don't remember most things at all well. If there wasn't strong emotion involved, you'll forget an event pretty quickly. If it was memorable, your brain makes a story out of your experience, and remembers the story, and maybe a few important details. When you remember it later, most of the details are reconstructed (made up) to fit the story. This results in amusing stories, but also in reliability issues in eyewitness reports.
Magicians make good use of these little shortcuts and assumptions our brain makes all the time; you do much of their work for them. The same goes for magicians' dark-side counterparts, psychics. There's a lot of money to be made by fooling people, and it's not that hard if you know how.
They way the mind works causes a number of cognitive biases that make it difficult to know whether something is real, or if you're just fooling yourself. Don't worry though, people have come up with a way to work around this problem. We've been using it (and refining it) for a few hundred years now, and it seems to work pretty well. It's called science.