Surface brightness of deep-sky objects and telescope specs
Although you have not given any information about your telescope, the Orion nebula is easy to see with almost any telescope, even under urban light polluted skies.

Surface brightness is almost always greater (ie fainter) than magnitude - so for example the total magnitude of the Orion nebula is about 4 (from memory) but you say surface brightness of 13.  The reason is that the area of the Orion nebula is quite large, at least when measured in arc seconds squared, and the eye/brain has some ability to integrate the light.  

This works both ways: there are objects, eg M33 and M101 in my experience, which have a magnitude that would make you think they are easy targets for small telescopes, but because the brightness is spread over a large area, they are difficult to see from a typical urban or suburban location.  The important measure in these cases is to compare the surface brightness with that of the background sky.

It's quite a complex topic, and Roger Clark's book "Visual Astronomy of the Deep Sky" has some useful discussion of this, and much more.