It's exactly what it sounds like. Imagine the old internet, but with no logins/user accounts/passwords/whatevers. You have your wallet keys and an ENS address, and every new internet application that ever gets developed integrates those two by default. And now you're expected to help secure the protocols you like to use, and you'll be rewarded for doing it -- this is the incentive layer that drives both development and adoption. Eventually, applications will integrate other applications, like how Alchemix automates Yearn Vaults for the user so that you can take loans that pay themselves off. Because now we're not just talking about applications for hosting and delivering content, we're talking about digital scarcity, i.e. money.
In a lot of ways, it won't feel terribly different from the old internet for most users. But the difference between logging into Aave to give yourself a loan and logging into your online banking portal to request a loan is massive, even if almost identical at a surface level. Uber without Uber inc. YouTube without Google.