What is it?
To provide a safe and trustworthy ad ecosystem for users, Google will require advertisers to complete one or more verification programs.
Advertiser verification program is Google’s unified verification program that consolidates identity and business operations verification in a single flow. The program comprises a series of steps that advertisers will be required to follow and complete. Under this program, advertisers will be asked to provide basic information about their business and identity.
Advertisers will be notified via an email and an in-account notification when they have been selected for the Advertiser verification program.
For more details of the Advertiser verification program - See this
How to do it?
You can directly go to "tools and settings" and click on "Advertiser verification" under the section "billing".
On the next screen you will see a button "Start verification", click on it to start the process. you will see further details to guide to through the process.
For more details - See official guide from google.