Laparoscopic surgery is what is commonly known as key hole surgery. This is done by special instruments and a video - camera system, and the operation is done by seeing it on a TV screen.

This gives an enlarged view of structures and the operation can be done more cleanly.
The surgeon's hands remain outside, a long cut it not required for accommodating the surgeon's hands.

Since the cut is small, the pain is minimized to a great extent. The cut sometimes is enlarged only for removal of organ or the part of it, which can be done by few centimeter incision. ( 4 -8 cms only.)

The cut for any open or conventional operation for kidney is about 15 to 25 cms to over a foot in obese person.

When reconstruction is done, i.e. organ is not removed, the largest cut is not more than 1.5 cm.

All the advantages are related to much smaller cut on the body and clear and enlarged vision under which the surgery is performed.
The biggest advantage is :-

NO UGLY SCARS and MUCH LESS PAIN
This means :-
Less amount of pain killers.
Early start of activity.
Early discharge.
Early recovery and early return to the work. 
Much less chances of wound infection and hernia.
Better body image
Less blood loss, since the vision of operative area is better.