The important thing about the hand is the gearing. The 40-tooth gears provide optimal torque and a large surface to attach the grippers. You can make stypes of grippers, these are designed to handle all sizes and weights of blocks.
The wrist is very simple: just an 8-tooth gear attached to a 40-tooth gear which is then attached to the hand. But it is very important. It provides the flexibility to pick the right angle for the hand so that you can set things down squarely.
Yet another pair of 8-tooth and 40-tooth gears. The wrist is attached to the inside of the 40-tooth gears. The counterweight is attached to the outside.
The turntable and worm gear assembly gives a gear ratio of 1:56 meaning it is slow but powerful enough to handle the weight of the entire arm, counterweight and load with ease.
The brick has two separate functions: it is heavy enough to provide the needed ballast to offset the weight of the wrist/hand and load, and it runs the hand. Its not obvious, but the hand is operated by the topmost touch sensor on the other brick but is cable to this brick.
Because there are 4 motors there are 2 bricks. The brick on the arm controls the hand, the console brick controls the wrist and arm pitch and yaw. For the wrist and arm you have a choice of modes selected by the arrow keys: left for hand/wrist down and arm left. right for hand/wrist up and arm right. The screens show exactly what sensor does what. The middle touch sensor controls the wrist, the bottom touch sensor controls the pitch of the arm and the end button controls the yaw. The top touch sensor controls the hand. But because that is actually controlled by the other brick. the mode can't apply. Instead, the direction of the motor alternated. The first time you press the top sensor the hand closes. Next it opens and so forth. In all cases, the particular motor runs as long as the sensor is pressed and stops when its no longer pressed. Please look at the program to see how this is done. It's a very useful and powerful technique.