How can I remove the white rectangle created when opening a file? When I open an image in Illustrator, I see a small rectangle in the center of the image and when I save the image using "Save For Web", Illustrator saves only the part within the rectangle but I want save all of the image.
That's the Artboard and you don't remove it. You can make it larger or smaller by going to
File > Document Setup and then click on
Your artwork must be contained in the Artboard. I'd suggest you read the link above from Adobe to get a better understanding of this concept.
To expand a little on what Ryan said, there is a faster way to edit your Artboards. Simply click on the
Artboard Tool and resize them to fit.
The even faster way is to automatically size your Artboard to fit your artwork.
I have this image of a tree that extends beyond my Artboard
Object > Artboards > Fit to Artwork Bounds
And there you have it: