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Project Abacus will use the phone's sensors to gather data about the person using it. Your typing patterns, walking gait, location, and face could all be matched against information Google knows about you.
The machine intelligence will calculate a "trust score" based on that data, determining how confident it is at any given second that you are the person intended to use the device.
If you have previously authorized your phone to access your account in a particular app you will be able to use that app without entering a password, just as long as your trust score is over the minimum for that app when you attempt to log in.
Google first announced the project at 2015's Google I/O conference. TechCrunch reports that Google clarified the timeline on Monday. Several "large financial institutions" will have access to Abacus in June, and if that goes well other Android developers will be able to use it by the year's end.