Hello!
What it does change is how users render the application. Instead of the legacy web client to render the navigation, dashboards, views and forms with a legacy rendering engine, the Unified Interface essentially renders the same customizations in a more modern, performant and user-friendly way.
To tackle that transition, you generally adopt out-of-the-box apps that are on the Unified Interface (e.g. Sales Hub) or you create new ones.
If you don't upgrade your users to the Unified Interface through the use of new apps, because the "Unified Interface only" mode is be automatically turned on in October 2020 (you can enable it earlier if you are ready), it will force the rendering on Unified Interface.
That's why it's very important to test your apps before that day.
In order to prepare, I recommend you go through the chapter 3: Transition of the Unified Interface Playbooks https://docs.microsoft.com/en-us/powerapps/maker/model-driven-apps/unified-interface-playbook
Henry