It is a strategy for getting required personnel for short or long-term projects avoiding costs of hiring new full-time workers. The staff augmentation vendor takes care of infrastructure and other costs related to having full-time workers. The business is the one supervising, leading, and managing resources.
A US-based startup makes an app and they need some additional resources to release the application before the deadline. They manage all the development inhouse. They ask a Belarus-based company to provide them with an iOS developer.
This employee remain on the staff augmentation company’s payroll, but still function as full-time employees of the US company.