PMO has various meanings depending on the industry, but in the business management realm, it stands for either Project Management Office or Program Management Office. To minimize the confusion, program management office is often written as "PgMO."
A project management office manages a company's projects. It organizes project teams, pulls in subject matter experts from needed departments, handles logistics and ensures projects are completed on time. The program management office oversees the departments in a program, one of which might include the project management office. Other departments could include team management, budgeting, recruitment and other areas that are needed to keep the program functioning.