Is the ML "looking" into its training data and "comparing" it with the input it has received and give a "mathematically" possible output?

Humans have this incredible skill that has helped us to evolve, "learning", where we are able to analyze input, recognize patterns, and make decisions based on our understanding of those patterns, right?
Machine learning is when computers do that with very little human influence
Also, I want to clarify my stance on Udacity, their Alumni Network that you gain access to after completion of any of their nanodegrees is incredible. I just don't feel that it can make up for how disappointing the course itself was as far as cost is concerned.

Humans take in input mostly in visual & audio formats. For instance, we grow up seeing the alphabets, A-Z and hearing them from our teachers. They train us on how they come together to form words so that we can learn and pronounce words later - even those we weren't taught in class.
Applying the same logic to ML.
ML encompasses the whole process learning from data without being explicitly programmed. The process of showing the data to the algorithm is called training - training the machine to visualize and recognize the data. So that it can also learn with from it and eventually be able to predict/suggest (pronounce) future results (words) without being explicitly taught. In short, computers learn to do things without being repeatedly programmed (instructed).