Google appears to be rolling out a new app called Pixel VIPs to Pixel smartphone users. The app's main premise seems to be to help you stay in touch with your favourite contacts and "never miss a moment from them."
The app was first spotted in April during initial testing in one of the dogfood builds. Today, the Pixel VIPs app was listed on the Google Play Store, but has been removed at the time of writing this.
Pixel VIPs helps you promote your favourite contacts (starred) to VIP status. You can have up to eight VIP contacts and elevate your communication with them with notes, birthday reminders, weather at their location, and get suggestions for things to do with them during your next hangout. The app also shows when you last contacted the person via phone or messages.

VIP contacts appear in your contacts list with a VIP tag. The setup page also suggests that Notifications from VIPs will bypass Do Not Disturb mode. Moreover, the app brings a new 4×1 widget that shows you all your VIP contacts. It's like the favourite contact widgets but three times wider.
You can customise the things you want to do with your VIP contact. The UI contains options like Movies, Spa, Sports and more, and you can select multiple interests. Surprisingly, it's deeply customizable.
Once done, Google will recommend these interests and activities pertaining to them in your location in a “Things to do together” section. The section appears as a Google Discover feed where you can like or dislike suggestions, and Google will tweak them for you.
The app appears to be rolling out gradually, so it might take some time before it appears on your Google Pixel phone.