Apple Inc.'s MFi Program ("Made for iPhone/iPod/iPad") is a licensing program for developers of hardware and App-Based accessories that work with Apple's iPod, iPhone or iPad.
MFi is Made for iPod abbreviation and this program is designed for the early iPod for the developers to design and develop third parties products to support iPod charge and sync.
Apple licensing program allows hardware developers to join their MFi and Apple is providing their referencing material, product library to help developers to pass certification training and compliance under Apple regulation in order to endorse MFi logo on their product packaging.
MFi Logo you can find in 3rd Party licensed product
Reference from Apple Official Guide