In addition to people and objectives, and scope, and a schedule, a project needs money to operate. Whoever brings in that money into the project is the Sponsor. So, in formal definition, the Sponsor provides funding or financial resources to the project.
In most cases, the sponsor generally would have an end goal in mind while providing the funding to the project. Thus, the sponsor will have a stake as well as interest in the project - the sponsor is thus also a Stakeholder. In fact, the sponsor is one of the most key stakeholders.
In most corporate projects, one of the sponsors will also drive the project to its initiation. However, in many other projects, people may individually initiate the project with minimal self-sponsorship (or self-funded), and then look for sponsors. A Technology project in an Enterprise to upgrade the entire hosting infrastructure may be sponsored by the CIO. On the other hand a Community may decided to work towards hosting an event and then look for Sponsors to provide additional funding support. Taking a third example, a newly formed Startup may decide to build a product and then look for sponsors in the Angels and Venture Capitalist communities. While these take different forms and may be called by different names, and may have different end goals, all of these are essentially forms of sponsorships.
So, the moment you accept money from someone (and it almost always has a string attached), you have essentially added a Sponsor onto your initiative. Recognize that and make sure that you take good care of your Sponsor, keep them happy and satisfied!