App note from NXP giving you an overview of Wi-Fi Alliance certification program and step-by-step procedure of the Wi-Fi derivative certification process. Link here (PDF)
Wi-Fi CERTIFIED™ is an internationally recognized logo of approval for products indicating that they meet the industry agreed standard for interoperability, security, quality and a range of application specific protocols. It ensures the product delivers best user experience.
The Wi-Fi certification program assures tested and proven interoperability among Wi-Fi devices. This certification gives confidence that Wi-Fi product bearing Wi-Fi Certified logo have passed rigorous interoperability requirements.
Authorized Test Labs(ATL) certification is important and most of the time it is the last milestone before the product launch.