It's my first encounter with 123D Design, and first time playing around STL/3D printing in general. I can't find much information about the grid. But I noticed, while trying to move it, you can actually raise it from the grid. Does this affect how it will be printed? Does the print have to be snapped to the ground for it to print properly? Or is the grid relative, used for approximation?
The position matters a lot if you use the default STL file without doing anything in the slicer. I've used 123D extensively and when I've inadvertently left a gap between the part and bed (and not snapped it to the bed in the slicer), the printer tries to print in mid air. Use "d" to "drop" the object to the grid. Different slicers have similar commands that will attach a face to the bed. I use Simplify3D.