Before trying to explain the statement made in the question, it is necessary to clarify some assumptions about productivity that are implicit in the question. To begin, productivity is more of a key result area in which managers need to perform well rather than a tool for improving performance. We can track the performance of managers in terms of productivity levels achieved. However, it does not make much sense to say that productivity helps to track progress. One more very important point - we don't use productivity to increase efficiency. Productivity and efficiency are closely, yet distinctly different things, and managers need to perform well in term of productivity as well as efficiency. Productivity focuses on increasing the outputs whereas efficiency concentrates on eliminating and reducing waste. Finally the concept of productivity and the general ways of achieving it remains same for both goods and services business. Therefore in this discussion I will not deal with these two types of businesses separately.
Yes, productivity, which measures quantity of total output produced, is very important for managers. Simultaneously managers must also aim to increase efficiency. In situations where effectiveness can be improved only at the cost of somewhat reduced efficiency, it is better to give preference to productivity. Let us say a workman can lay 1200 bricks in 6 hours in a day giving a productivity of 200 bricks per man-hour. If the working hours are increased to 8 hours a day the output is increased to 1520 bricks giving a productivity of 190 bricks per man-hour. In a situation like this the efficiency of the workman has reduced, but the total productivity has increased by increasing working hours. If a workman is paid by wages according to number of bricks laid. he will improve his total earning by working 8 hours a day rather than 6 hours, even though this reduces his efficiency.
To improve the productivity, the managers need to set targets for generating outputs in terms of suitable variable such as total profit, net sales, or total quantity of goods to be produced. Of course a service organization will use some measure of service provided rather than goods produced. For example an airlines may fix targets of production in terms of passenger seat miles flown by each aircraft, and the sales target may be measured in terms of passenger miles flown or revenue generated.
While the question appears to be requesting either goods or services, the answer can be both. It is crucial to understand productivity from an economic standpoint. Whether one is using human capital or goods/components as capital, productivity can be measured. Often it is challenging to not be subjective in the accounting, but it can be used as a tool or set of tools.