PEO is the acronym for Professional Employer Organization.  The purpose of a  Professional Employer Organization  is to manage the human resources, the payroll and administrative expenses of a business, called the Client Firm.  Technically the employee works for this organization as the agency assumes responsibility for recruitment, wage, tax reporting and personal recordkeeping for all the employees. That means that the agency can terminate an employee if it is necessary.

The employees working under this arrangement are called "Leased Employees".

While the agency is responsible for tax withholding and reporting, it still the client firm (business) responsibility to ensure that is done properly.