Machine learning is a subfield of artificial intelligence. We know that we can never truly create machines that actually "think" but we can supply machines with enough data and models by which sound judgment can be reached. Machine learning focuses on creating autonomous systems that can continue the process of decision making, with little or no human intervention.
In order to teach the machine, we need data drawn from the real world. For instance, to shift through which e-mails constitute spam and which ones don't, we need to feed the machine with samples of each. After obtaining this data, we have to run the data through models (algorithms) that will use probability and statistics to unearth patterns and structure from the data. If this is properly done, the algorithm by itself will be able to analyze e-mails and properly categorize them. Sorting e-mails is just one example of what machines can do if they are "trained".