TL;DR The 737 design is super, super old and they wanted to install new engines on it that are more efficient and powerful. These engines are much bigger than the engines that were initially installed, meaning they had to be installed further up the wing in order to ensure adequate ground clearance. Unfortunately that changes the flight model of the airplane and makes it prone to pitching up, especially during take off. Pitching up too far can cause a stall and result in a crash. MCAS was designed to detect this pitch up and counter it with a pitch down.
It's entirely possible, even likely I would say, that the majority of pilots would intervene before a stall is ever reached in a scenario where MCAS would kick in. I think you could fly this plane for hundreds of thousands of hours without incident without MCAS. Unfortunately, there have been cases (AF447) where the pilots were so confused/tired/inexperienced that they ignored the stall horn and let the plane stall and crash. MCAS was meant to address situations like those but tragically it only made things worse.
The other thing is that Boeing didn't want to have to re-certify this aircraft with the FAA, as that would also require airlines to train their pilots for this new aircraft type. Note that the whole purpose of the MAX was to compete with the A320neo, and re-certification would have taken a long time and cost a whole lot of money. This would negate the purpose of the MAX in the first place. MCAS allowed Boeing to "pretend" the 737 MAX was the same exact airplane as the 737NG (which the MAX was based off, I believe), and thus pilots didn't need additional training outside of a 30 minute iPad session.