The Boeing 737 Max 8 is not an inherently unstable aircraft. There are plenty of military aircraft that are inherently unstable and require fly-by-wire in order to keep them in the air. The F-117 is a perfect example of this. Even with its computers and fly-by-wire systems, it is still nicknamed the Wobbly Goblin. That instability gives them better performance. An inherently stable aircraft doesn’t want to turn as quickly as an inherently unstable plane with computer stabilization. Since passenger jets generally aren’t trying to outmaneuver other aircraft, there isn’t much need for this type of instability on them.
The Boeing 737 Max 8 has bigger engines than the previous 737s, and in order to make them fit, they had to move them forward and upward. While the 737 Max 8 is not inherently unstable, in a low-speed, nose-up attitude, and possibly a steep turn, the engines tend to want to rotate the nose further up, which could cause a stall. The MCAS system that you are hearing a lot about is designed to prevent a stall in this rare case, and only this rare case, of low-speed, nose-up, flaps-retracted condition.
If you aren’t in a low-speed, nose-up attitude or a steep turn, the MCAS system should not be engaging. It’s not necessary to keep the plane flying in most conditions.
Computers taking control of airplanes is nothing new in commercial aircraft. Airbus tends to have even more computer controls than Boeing. There is an old joke that planes are moving towards having only one pilot, a computer, and a dog. The computer flies the plane and the dog is there to bite the pilot if he attempts to touch anything in the cockpit. 
The problem in this case is that the MCAS system seems to be triggering when it shouldn’t, possibly due to a fault in a single sensor. The MCAS system rotates the entire rear wing of the plane to pitch the nose down, and yanking back on the control column only pushes the little flaps on the ends of those wings back up, meaning that the MCAS can push the nose down a lot harder than the pilots can pull it back up.
Boeing published a procedure to get out of this problem. Switch off the MCAS and trim the plane (rotate the entire back wing) back up so that the plane flies level. The problem is that the Ethiopian pilots apparently did just that and it didn’t work. If you switch the elevator (rear wing) controls completely off, you can still crank the rear wing’s pitch angle by hand, but it is apparently difficult to do, possibly next to impossible if you are in a high speed dive caused by the plane pitching down on you.
This video from Mentour Pilot explains why the 737 Max 8 has the MCAS system.