What Machine Learning Really Is
Learning rules from examples
Normal programming means writing the rules yourself. If the email contains this word, mark it as spam. Machine learning flips that around. Instead of writing the rules, you show the computer many examples and let it work out the rules on its own.
You hand it thousands of emails already labelled spam or not spam, and it figures out the patterns that separate the two. The output of that process is a model, which is just a function that takes an input and returns a prediction.
Why bother
Some problems are almost impossible to write rules for. Nobody can list every rule that tells a cat from a dog in a photo, but we can gather plenty of labelled pictures. Whenever the pattern is real but too messy to spell out by hand, learning from data wins.