There are two main ways in which the capital stock can change and, thereby, improve labor productivity. The capital stock can be increased or it can be improved.
One way to improve labor productivity is to have more capital stock. When there is more capital stock, more workers can use technology to increase their productivity. Let us imagine, for example, a gang of workers who are building the frames for houses. Let us imagine that all of them have hammers except for one who has a nail gun. If more nail guns become available, the workers will be able to frame houses more quickly. This will increase their productivity.
A second way to improve labor productivity is to improve the capital stock. Let us think about the workers framing the houses once again. Imagine that the nail guns they have do not always shoot the nails hard enough to completely embed them in the wood. The workers must then take time every now and then to hammer in the nails where they did not completely embed themselves. Now imagine that the capital stock improves. New nail guns are made that embed the nails perfectly every time. Worker productivity rises because no time is wasted on pounding in nails that are sticking up.
Thus, labor productivity can be improved by increases in the capital stock and by improvements in that stock.