When you select the help option at the bottom of the drop-down menu, the app will no longer shoot you out to a help page tucked inside a web browser. Now you can view that same content directly inside the app. The posts won't look drastically different, but at least Google+ will stop passing you around like a basketball downcourt.
Left: old, Right: new.
As you may have noticed, the top level topics aren't the same on the Google Help website as those that appear inside the app. No matter. If you perform a search, the same content comes up.
All of the other changes we've noticed thus far are too minor to draw attention to. A change of wording here. A few new labels there. If you see anything major, give us a holler.
The APK is signed by Google and upgrades your existing app. The cryptographic signature guarantees that the file is safe to install and was not tampered with in any way. Rather than wait for Google to push this download to your devices, which can take days, download and install it just like any other APK.
File name: com.google.android.apps.plus-126.96.36.199566200-413957129-minAPI19.apk
Version: 188.8.131.52566200 (413957129)