The general reason is that multinational firms possess something leading (e.g., a famous brand, a cool design, a secret recipe, a technology can boost productivity, etc.), and they want to exploit this proprietary advantage in international markets. Enrich it
The purpose of setting up foreign subsidiaries vary across different industries, e.g., Auto, Consumer Electronics.
Vertical vs. horizontal
Greenfield vs. M&A
R&D vs. Production
Offshoring/Outsourcing
ODM (Original Design Manufacturer)
Contract/Sub Contract manufacturing
OEM (Original Equipment Manufacturer)
EMS (Electronic Manufacturing Services) or ECM Contract
Order by the ability to invent new variety by manufacturer
ODM > EMS > OEM > Sub Contract