Office UI Fabric is the framework for building the Office and Office 365 user experience. This is a bit like Twitter Bootstrap, a framework primarily for CSS and UI. It was designed originally to help Office add-in developers get the look and feel of Microsoft Office applications. You don't have to use it, but if you want to build a consistent user experience for your web parts--something that fits right into the other components that are available in SharePoint sites--then Office UI Fabric is the way to go. Fabric Core includes the styles we have already used, and Fabric React includes a wide array of components that are built with React.
The idea here is not only to use the same design language and look and feel that Office 365 is using, but also to utilize reusable patterns.