Basically, hiring the right person increases the productivity of a firm while hiring the wrong person decreases it.
If a firm hires a very good candidate for a job, that candidate will add a great deal to the firm. He or she will work well and will create a relatively high amount of value for every hour he or she works. This is because he or she is well-suited for the job. A person who is less well-suited will not do such a good job and will not create as much value (will work slower or create an inferior product).
If the person hired is so bad that they must be let go, the firm incurs further costs. They have lost the time and resources used in training the person and they must now expend more time and resources in hiring and training a new person. This, too, decreases their productivity.
The post above covers the idea pretty well, I just wanted to add that in many business environments, from fast food restaurants to marketing firms, the employee functions as part of a team. Their contributions to that team are not only reflected then in their own productivity levels.
A "bad hire", or someone who either is not capable of performing well or chooses not to because of their own lack of work ethic, etc. does not contribute their own productivity to the team, but they also tend to limit others' productivity. Other workers must "pick up the slack" for specific tasks that are not done, especially those the successful completion of their own tasks are dependent on. They are forced to do more than one job, perhaps something they are not as qualified for and the productivity and success of the entire team and company suffers. This is called a productivity gap.
With a good hire, an efficient, talented addition to the team can accelerate others' productivity, but can also serve as healthy competition with co-workers for recognition, promotion, or simple sense of accomplishment and pride. This makes the entire team work more effectively, and affects their intrinsic motivations.
From the eNotes link below:
Productivity Measures for Individuals and Teams An individual's productivity is measured by that person's potential to reach the highest level of productivity possible. That is, a person has certain skills that determine his or her level of capability (an engineer's skills, banker's knowledge, etc.). An individual's experiences and education usually determine his or her skill level regarding a particular job. Other factors, such as a positive environment (working with a good team, having a good boss, liking the physical surroundings in the workplace, being appreciated, etc.) and how motivated one is to do a job, also contribute to productivity. When several individuals come together to work as a team, the team's productivity or the effectiveness of the team is the sum of individual efforts toward achieving a desired goal. Several factors (motivation, expertise, working conditions, team compatibility, potential, etc.) influence the level of productivity achieved.