If you've never shot 35mm film before this could really be confusing because of the lack of reference.

See the photo below:
Compared to a full-frame (FX) sensor, you're basically "cropping" or using a smaller part of the image when you use a DX or crop sensor. DX lenses are made to only cover the area of the smaller sensor. You'll probably get vignetting (darkeninng of the corners) if you use one on an FX camera, unless it detects that it has a DX lens attached.

If I have a 70-200 lens on a full frame Nikon D-700 it gives about the same angle of view as the 50 -150 Sigma on a D300 (actually 75- 225)

Read this link from Kan Rockwell's site: http://pogue.blogs.nytimes.com/2006/11/21/21pogues-posts-2/

Big prints, in my experience, don't need more resolution as they are intended to viewed from a greater distance. I regularly make prints up to 50 inches wide on our wide format printers for conventions and displays. We scale them up from their native resolution in Illustrator nad print from there. Love the Epson for the best output.

I tried a couple of Sigmas lenses a long time ago and they were...cra..not very good, to put it kindly.
Now I have two that I love- the unfortunately discontinued 50-150 2.8 (a fantastic portrait lens for DX lenses) and the 10-20.
Have used the 105 macro as well and it's right up there in quality.

Great site- Thanks J Pat
Here is a direct link to that particular question:
http://www.expertphotography.com/5-steps-to-understanding-the-crop-factor