It may have several meanings, but in my experience MEP is usually short for a firm that handles Mechanical, Electrical, and Plumbing on a construction project. There may be two different companies that represent the MEP design and the MEP installation. However, it is common in the design world to have the mechanical and plumbing to be one company and electrical to be a separate company. Mechanical usually refers to air conditioning, heating, and maybe other mechanical devices such as pumps. The MEP may also be responsible for fire protection systems that spray water or other chemicals, however this might be a specialty contractor depending on the project. I believe elevators are also a specialty trade that does not typically fall under the general MEP category.