A cost center is a subunit of a company that is responsible only for its costs. Example of cost centers are the production departments and the service departments within a factory and administrative departments such as IT and accounting.
A profit center is a subunit of a company that is responsible for revenues and costs. Often a division of a company is a profit center because it has control over its revenues, costs, and the resulting profits.
Cost centers and profit centers are usually associated with planning and control in a decentralized company.