Understanding machine learning

Aren't we taught that computer systems have to be programmed to do certain tasks? They may be a million times faster at doing things but they have to be programmed. We have to code each and every step and only then do these systems work and complete a task. Isn't then the very notion of machine learning a very contradictory concept?

In the simplest ways, machine learning refers to a method of teaching the systems to learn to do certain tasks, such as learning a function. As simple as it sounds, it is a bit confusing and difficult to digest. Confusing because our view of the way the systems (computer systems specifically) work and the way we learn are two concepts that hardly intersect. It is even more difficult to digest because learning, though an inherent capability of the human race, is difficult to put in to words, let alone teach to the systems.

Then what is machine learning? Before we even try to answer this question, we need to understand that...