There are many Apps that can be downloaded to different devices (game apps like Candy Crush, language apps like Duolingo, entertainment apps like Netflix, etc.) Most Apps allow you to log in using a username or email address and a password that you create. They also allow you to log in using your Google or Facebook or other social media accounts. Using one of the social media accounts allows you to, for example, keep your level in Candy Crush, watch history on Netflix, etc. on which ever device to play it on.
According to the message you received, most major trusted Apps that you have used your Google account to log into should still work but there are thousands of Apps out there that are less trustworthy and those may no longer work. You can still access them but you will have to create a new Username and Password to access them in the future and use your new credentials to log into that App on each separate device.