A Visa Sponsorship means someone is Sponsoring you to support your application for a visa.
Sponsor means to support, to take responsibility for.
Visa sponsorship is when a company or person from a country supports your application for a visa for that country. There’s a lot of variability. This could be a company sponsoring you for a work visa to come and work for them, it could be your spouse sponsoring your application to immigrate and live with them, or it could be an organisation that you’re visiting that sponsors you for a short-term visitor’s visa.
The one wishing to obtain a visa sponsorship to enter a country must have a reputable citizen or group from the country you hope to enter that is willing to provide assurance that they will assist with your financial and social responsibilities while you are in their country. They must have full citizenship. They must be ‘investigated’ by the country you are hoping to obtain a visa for. The investigation would consist of financial and the ability to be able to maintain your stay in the country. There past records both legally (and if they had provided prior sponsorship) would also be taken into consideration before visa sponsorship ability, approval and visa approval and contained documentation (including signatures of both parties to insure understanding of responsibilities) would be granted.