See below. Nonobstructive kidney stones are those that sit inside the kidney. When they move around and go into the ureters is when they become obstructive, and are more likely to cause problems.
Kidney stone. Kidney stones up to 5mm in size will predictably pass on their own with some degree of pain. Just drink plenty of water so you produce a lot of urine, dilate those ureters and allow the stone to pass. It may hurt while it's on its way out, but it'll pass. Bigger stones will likely get stuck and will cause tremendous pain and will have to be removed by lithotripsy or cystoscopy.
Kidney damage. Obstructive stones can damage the kidney involved by causing back pressure. The non obstructive stones usually do not damage the kidney. Either stone may or may not be painful.