In 1999 psychologists Daniel Simons and Christopher Chabris published a famous experiment on human focus and attention. Before you read further, you might want to do the experiment yourself -- it is a fairly simple task to measure your attention and focus on a moving target. It won't take long, and seeing the setup with your own eyes will allow you to skip the next paragraph. You can see it on YouTube here.
In this experiment, six grad students are divided into two teams (the black-shirts and the white-shirts), and pass two basketballs around a small room. The test subjects are asked to count how many times the team dressed in white pass the ball -- not a trivial task, as the room is small and teams mill about constantly. The clip is only about 60 seconds long (the shorter version, in the link above, is only 30 seconds long), but getting an exact count is tricky.
If you haven't watched the clip already, now is a good time to do so.
This study has been repeated many times, with different videos, set-ups, and across different groups, and it is pretty consistently found that only about half of the test subjects notice an oddity midway through the video. The other half miss it completely. This effect is called inattentional blindness, and turns out to be pretty common even outside of staged psychology experiments.
Those that see the gorilla are amazed that anyone could miss it, and those that miss the gorilla are amazed that they had missed something so obvious. Pretty much the same thing can be said for motorists who don't see bicyclists, doctors who don't notice obvious abnormalities on x-rays, and audience members who fall for a magician's misdirection.
Perhaps the single most referenced cause of inattentional blindness is using cell phones when driving. It appears that using a cell phone -- including hands free phones and using phones to text -- is a major cause of drivers missing important changes in traffic. Most of us can easily drive and use a phone at the same time, and have no problem handling normal traffic conditions without trouble. However, the slight distraction of using a phone is often enough to make us blind to unexpected pedestrians, motorcycles, bicyclists, stop signs, and deer.
Inattentional blindness has been demonstrated in a number of experiments, most of them not involving gorillas... and obviously, has relevance to our life in many non-great-ape related situations. Gorillas in Our Midst has become one of the best known examples of the phenomenon simply because the gorilla is so very visible that it is hard to believe that anyone missed it -- including yourself.
Perception. 1999;28(9):1059-74. Gorillas in our midst: sustained inattentional blindness for dynamic events. Simons DJ(1), Chabris CF.