'project sponsor' basically means the person/company/department who is responsible for creating, planning and making sure the project happens.
Normally, the 'project sponsor' isn't involved in actually running the project (which is the responsibility of the project manager), but they are ultimately responsible for its success or failure. So they are keenly interested in making sure that the project is a success. As a result, project managers normally report all progress directly to them.
In a project to build a new road, the 'project sponsor' could be either the local government or the department of transport.
To learn more vocabulary connected to projects, you can do a free online exercise on project related vocabulary.