Just as a neck strap keeps a camera attached to your neck, the Nikon AH-4 Leather Hand Grip keeps a camera attached to your hand.
A neck strap has a tendency to get in the way when it is not actively being used - and can even be the cause of a dropped camera if the strap catches on something unexpectedly. If you are going to be primarily holding the camera in your hand, it may make more sense to use a hand strap. The hand strap helps control and support the camera - and helps prevent it from falling to the ground.
The quality of the Nikon AH-4 Leather Hand Grip is very nice. It is priced accordingly - somewhat high.
Unlike the Canon E-1 Handstrap, the AH-4 includes a camera body plate adapter that threads into the tripod mount on the camera body. The adapter includes a tripod thread of its own. This attachment method allows the AH-4 to be mounted on camera bodies with and without battery/vertical/portrait grips. In addition, the body plate allows one side of a neck strap to be attached. Since the hand strap utilizes one of the neck strap attachment points, this feature allows both straps to be attached simultaneously.
When attached to a full-size pro body such as my 1Ds Mark II (as seen in the picture above), there is only a small amount of excess attachment strap length - it works great. When attached to a smaller body such as a Canon 30D, there is far more excess strap. In this case, the excess strap wraps back around the hand strap and hook & loop attaches to the other side. Good solution again.
The AH-4 provides excellent support with its solid 3-way strap covered by nice grade soft leather. The lower left attachment quickly releases to allow easy in and out of the hand strap. The Nikon AH-4 Leather Hand Grip is a much nicer solution than Canon's E-1 Handstrap. If you are going to be using a hand strap much, the AH-4 deserves your attention.