Machine learning: introduction, monumental failure, and hope

Wikipedia tells us that Machine learning is, "a field of computer science that gives computers the ability to learn without being explicitly programmed." It goes on to say, "machine learning explores the study and construction of algorithms that can learn from and make predictions on data -- such algorithms overcome following strictly static program instructions by making data-driven predictions or decisions, through building a model from sample inputs." What does it mean to learn from inputs without being explicitly programmed? Let us consider a classical machine learning problem: spam filtering. Imagine that we know nothing about machine learning, but are tasked with determining whether an email consists of spam or not.