Often quoted, almost always misquoted
Focal length of the human eye is around 22mm. Field of view of the human eye is over 180 degrees. Angle of view of a 50mm lens on a full frame camera is 46 degrees.
However, when you look through a lens of around 50-60mm the image appears around life size (depends on the camera) so when you put the camera to your eye it appears as if you are recording a section of the scene as you're seeing it. As a result, the perspective generally looks about 'right'. It usually looks 'natural'.
Also, about 40-70 degrees is the angle of view of the most active area of the eye - the area of highest awareness, the area you scan with your eyes before turning your head, that kind of thing. Even though you can actually see far more in total, while the actual area you're focusing on is tiny - like just this typed word you're looking at now, and maybe a couple either side.
So, while the 'same as your eye' bit is literally untrue, there is some truth in it. Cartier-Bresson famously used a 50mm lens on his (full frame) Leica for those wonderful street images of Paris for this reason. Which is a great excuse to link one of my favourites - just like he saw it walking past
http://1.bp.blogspot.com/_0AZZvuenG...U/kNmGTGxGDVo/s1600/henri_cartier-bresson.jpg