Microsoft 365

The Microsoft 365 app is a dashboard, or front-end, to all of the work you perform in the Microsoft Office productivity apps and services. It's a simple app with app shortcuts, document templates, tutorials, and quick access lists of your recent, pinned, and shared documents and other content.

Where did it go?
The Microsoft 365 app was previously called the Office app. It was renamed as part of a broader rebranding effort where most of the products and services that used to be part of the Office brand are now consider part of Microsoft 365. The Office name is still used for the familiar desktop and web applications like Word, Excel, and PowerPoint.
The Microsoft 365 app might look familiar: Microsoft offers the same basic user experience on the Microsoft 365 website and the Microsoft 365 mobile apps for iPhone, iPad, and Android, and its lists of recent, pinned, and shared documents work a bit like the Recommended area in the Windows 11 Start menu and the File Explorer home page.
Understand Microsoft 365
Microsoft 365 is the umbrella brand for Microsoft's productivity apps and services that includes, among other things, a family of consumer and business subscription services. Some Microsoft 365 capabilities are available for free to anyone with a Microsoft account---there are free but somewhat limited versions of Word, Excel, PowerPoint, and other Office apps on the web, for example---while other, so-called premium features require a paid subscription.
You can compare the consumer Microsoft 365 subscriptions on the Microsoft website.
The Microsoft 365 app in Windows 11 will behave a bit differently depending on whether you are a subscriber and whether the Office desktop suite of applications is installed on your PC. If those applications are available, the app shortcuts on the left and the templates under "Create New" will launch the relevant desktop app when selected. If not, your default web browser will open and navigate to the web version of the relevant app.

Well, for the most part. The Microsoft 365 app will oddly use web apps sometimes even when you do have a desktop version installed. This can make using the app a bit frustrating.
There is no way to configure this behavior. Indeed, there is no way to configure any aspect of this app. Its settings interface is basically empty.
Access your Office apps
The Microsoft 365 app provides shortcuts to the core Microsoft Office apps---Word, Excel, PowerPoint, Outlook, OneDrive, Teams, and OneNote---in its navigation pane on the left. These are all pretty obvious, but there are other items there of interest:

Create. Click this button to access a broader set of templates than is available in the home view. This is briefly described below.

Apps. Click this button to access a broader set of apps than is available in the navigation pane, including several web-only utilities.

If you do have a paid Microsoft 365 subscription and the Office desktop apps are not installed ...