That means if you have a Google account you use to sign into Gmail, YouTube, or any other Google service, you'll be able to carry over that information to sign in to non-Google apps. Similar to Facebook Connect apps, Google+ Sign-In will prompt you to review which permissions you're approving about who can see your activity and how much data the app gets about you.
One particularly convenient feature of Google+ Sign-In for Android users: When you sign in to a website using your Google account, a prompt will allow you to install the mobile app version on your Android device.
In its blog post, Google emphasizes current issues with "frictionless" sharing, when apps post or "spam" your activity updates to others, and vice versa, with abandon. So with Google+ Sign-In, Google promises you easy control over what you do and don't want to share, and with whom. It also promises friends' app activities will only show up when they're relevant to you. To that end, you'll now start to see a new "interactive" post in Google+ that lets you not only see what your friends are up to on other apps, but participate as well. This is similar to the concept behind, for example, Facebook's Spotify integration, which lets you not only see which songs your friends are listening to, but also transports you to Spotify so you can listen to the song yourself.