After you follow a business, all of their updates then appear in the new "For You" tab of Google Maps. In this area, you can keep track of all the notable updates and promotions offered by the various companies you follow in the app.
This is a feature that has been on Google Maps for Android since last fall, and is now just rolling out to Apple device owners. It works in conjunction with Google's revamped My Business app, which also launched last fall, allowing businesses to post updates to their profiles on Google in the same fashion as a Facebook post or Tweet [Direct Link].
Because of this, many users can now turn to Google Maps as a sort of alternative to keeping up with their favorite local spots, if they've turned away from Facebook in recent months. These posts on Google Maps can include notifications about upcoming events, special offers for customers, menu updates, and more.
The Follow button in Google Maps is rolling out to all iOS users starting this week.