Google Inbox has been available for only a week, and Google is already tweaking the Android app. Not much, of course - sweeping changes don't come that fast. But as with the recent updates to Newsstand and other apps, Google is getting a little more consistent with its Material Design standard. There don't appear to be any huge shifts in functionality in this update, though users with multiple email accounts will certainly appreciate at least one.
What's New
If you happen to be using Android 5.0, either on a shiny new Nexus device or via the developer preview, Inbox now blends the color of the action bar into the status bar. Naturally, this doesn't work on older versions of Android. [Ed. note: this would probably be possible in older versions of Android, as mentioned by some commenters. Google is probably just using the solid status bar color option in Android L, which doesn't work on older software builds (where the same thing is achieved with a more resource-intensive transparency effect).]
Left: Inbox 1.0. Right: 1.1.
The slide-out navigation menu now covers the action bar when it fires. Google has been somewhat haphazard in deciding where the menu and the bar sit in the Z-order of the app's visual layout; presumably someone made a push for more consistency.
One last thing: opening the menu and then sliding from left to right on the upper section, where your email address and personal profile image sit, will automatically scroll through multiple email accounts. If you have only one email connected it does nothing, if you have more than one, it switches Inbox to the next account and closes the menu. This is consistent with the design of Gmail 5.0.
There may be other changes as well, especially beneath the hood, but so far we haven't seen any. You still need an invitation from Google or a friend to access Inbox on Android and on the web.
Download
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.inbox-1.1_(78614022)-5608659-minAPI16.apk
Version: 1.1(Android 4.1+)
MD5: 1155eef95328c96946a133d411056fc8