The Global Food Safety Initiative is a Forum which makes up a global food network made up of approximately 400 retailers and manufacturers who are food safety experts from around the globe.
This group of experts meet regularly to share knowledge and promote a harmonized approach to managing food safety across the industry and across the world.
GFSI does not offer any certification of its own but evaluates different food safety standards against a set of criteria they have developed. They use this criteria to determine whether the food safety standards are equivalent and certification would be acceptable. If so, that food safety standard is recognized by GFSI.
This means that they would like you to be certified to a food safety standard that is recognized by GFSI. This gives you the freedom to select which food safety standard to implement in your company as long as you select one from their list of options.
Once you select the standard, you would implement it in your company and then have a 3rd party audit by a certification body. Upon successful completion of the audit, you will be granted your certificate.
So, although many people use the term "GFSI Certified" that is not correct and there is no "GFSI Certification" but what they mean is "Certification to a GFSI recognized standard".
Check the GFSI website (mygfsi.com) for the most up-to-date list of recognized standards.