Binding usually is narrow, but often there is a border between the patches and the binding, and the border (or borders) can be anything from about 1/2" up to 6"-8" wide.
Ideally you should have left the seam allowances on all around the edge, but there are no quilt police and if you cut them off it's because you wanted it that way
The edges of a quilt are what get most wear, thus a lot of people like to make a
double binding.
I like my bindings quite firm and use 2" strips folded in half. Others like then a bit looser/softer and use 2.5" strips