Machine learning is just trial and error on steroids. A program can try the same process millions of times to find the system that works. You give the program some rules and a goal to achieve and it tries over and over and makes adjustments that get it closer to the goal.
If there is a dot on the left side of the screen and you want it to go to the right side of the screen in the most efficient way possible, a machine learning algorithm would try sending the dot in each direction and it would find that the dot that goes on pixel to the right gets it closer to the goal more efficiently. Then it would do that step over and over again. Pretty quickly it would show you that the fastest way to do it is a straight line to the right. But if you want it to get through a maze or win a game of chess or figure out the stock market, it would have a much more complicated task that would would require a lot more trial and error.
CGP Grey has a good video on machine learning that explains it nicely.
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