It's actually a measure of the angle over which light can be collected, and it's defined as the sine of the half-angle. For example, if you want to launch light into a fibre-optic cable with NA 0.5, the light needs to be angled 30 degrees or less with respect to the cable (since sin(30) = 0./5); any light with a greater angle won't undergo reflection and so simply shoot out the side of the fibre (conversely, light at smaller angles will be reflected and so go bouncing down the cable until it comes out at the far end - again with a 30 degree half-angle).