Just think of how much more accurate a surgeon can be on immobile objects (say, your bones or joints when a limb is immobilized during surgery). If you work on something like embroidery with your own hands it's hard to get things exactly where you want them and magnification of your view can only help so much. Consider in contrast working on an image in a program like Photoshop where you can magnify the image on screen, affecting not only your view but also the size of mouse movements required to draw a given line. These surgical assists must work a lot like a zoom function, where not only can the doctor enlarge the view of what they're looking at but also translate gross hand motions into tiny robot motions.
Another cool thing is the ability of the robot/camera system to compensate for motion far faster than a human can. In theory (I don't know if da Vinci does this yet but there are hints it does), the surgeon can select a recognizable feature inside the patient and instruct the system to compensate for motion. Then the surgeon would see a steady image from the camera, but also the robot arm performing some action would compensate for the motion with the same algorithm, also compensating for the surgeon's tremor.
The literature describes more benefits: the ability to work through much smaller holes in your outer skin (under one inch rather than 8-10 inches), which has just got to be an improvement. The claim that they can cut recovery time from 12 weeks to a day or so is an incredible deal in reduced hospital costs (decreasing surgery time, reducing hospital bed and medication usage during recovery). Since each day in a hospital costs so much, it seems easy to imagine saving 10,000 per surgery (that's only a couple weeks of hospital recovery, I estimate). Thus in 100 surgeries, possibly under one year, the machine pays for itself.
FDA approval for some types of surgery happened in 2000, and today according to the radio ad these systems are available in my area, so they're not just research any more and I'm behind the times already. I know this is gushing, but I love technology like this.