It depends on what you mean by "job centre."
This is the official job center for the state of Wisconsin. This is run by the state. Each state in the US collects "unemployment insurance" from each worker and uses it to pay benefits to people who lose their jobs. They also run centers such as this to help people find new work. This can include training and help in creating resumes, etc.
There are also private agencies that help to place certain type of workers in positions. They are usually paid a fee by the companies that use their services to find qualified people to fill their vacancies. These are referred to colloquially as "headhunters."
Finally, there are private companies that provide labor services to other companies by hiring workers and contracting out their services to companies that need them. These are called "temp agencies," meaning they place workers in "temporary" positions.