Engage's connection with Google Customer Match can be used to target your communication on Google Search, Google Display Network, Youtube, and Google Shopping. The connection is created by connection a Google Ads account in the Targeting section of Engage.
When creating this connection, the Engage user will be faced with a popup like this:
Clicking "Learn more" on the first option above will show this kind of popup:
The layout and content of this popup is updated constantly by Google, so it might look somewhat different. What it's asking is if Engage can interact with the Google Ads account of all contacts in your Engage environment, present and future, and use their data in the way described above. How that interaction works on a detailed level will depend on how the contact has configured their own Google Ads account. This is just a blanket permission allowing Engage to try.
This access is needed because the integrations endpoints used to read and write to the Google Customer Match service have no lower granularity level, so all the things in the image are requested by default. Engage, however, only uses a small fraction of them.
In short, this is just a standard step when working with Google Ads in Engage.