How does it work?

Boeing explains :

The Maneuvering Characteristics Augmentation System (MCAS) flight control enhanced flight control law incorporates angle of attack (AOA) inputs, limits stabilizer trim commands in response to an erroneous angle of attack reading and provides a limit to the stabilizer command in order to retain elevator authority..

A pitch augmentation control law (MCAS) was implemented on the 737 MAX to improve aircraft handling characteristics and decrease pitch-up tendency at elevated angles of attack. It was put through flight testing as part of the certification process prior to the airplane entering service. MCAS does not control the airplane in normal flight; it improves the behavior of the airplane in a non-normal part of the operating envelope.

Boeing’s 737 MAX Flight Crew Operations Manual (FCOM) already outlines an existing procedure to safely handle the unlikely event of erroneous data coming from an angle of attack (AOA) sensor. The pilot will always be able to override the flight control law using electric trim or manual trim. In addition, it can be controlled through the use of the existing runaway stabilizer procedure as reinforced in the Operations Manual Bulletin (OMB) issued on Nov. 6, 2018. 

Boeing Statement about software

Boeing has been working closely with the Federal Aviation Administration (FAA) on development, planning and certification of the software enhancement, and it will be deployed across the 737 MAX fleet in the coming weeks. The update also incorporates feedback received from our customers.

The FAA says it anticipates mandating this software enhancement with an Airworthiness Directive (AD) no later than April. We have worked with the FAA in the development of this software enhancement.

It is important to note that the FAA is not mandating any further action at this time, and the required actions in AD2018-23.5 continue to be appropriate.

Lion Air Case report (Wiki)

On 7 November, the NTSC confirmed that there had been problems with Flight 610’s angle of attack (AoA) sensors. Thinking that it would fix the problem, the engineers in Bali then replaced one of the aircraft’s AoA sensors, but the problem persisted on the penultimate flight, from Denpasar to Jakarta. Just minutes after takeoff, the aircraft abruptly dived. The crew of that flight, however, had managed to control the aircraft and decided to fly at a lower than normal altitude. They then managed to land the aircraft safely and recorded a twenty-degree difference between the readings of the left AoA sensor and the right sensor.