Post hoc is from the Latin for "after this"; the long form of the phrase is post hoc ergo propter hoc, "after this, therefore because of this."
A non-controversial example is "I just washed my car, so of course it began to rain." Rain is not caused by car-washing, but the car owner connects the two events. The person down the street did not wash her car, and it is raining on her car too.
This logical fallacy is often used by the media to misreport the results of correlative studies. For example, if a study showed that 70% of kids who played violent video games grew up to criminals, whereas only 20% of kids who played nonviolent video games did, the media might report "violent video games make kids into criminals", which is not supported by the evidence. (The criminals may have played violent video games more because they were criminals! There's no evidence that the games caused their behavior to change.)
Post hoc reasoning is related to magical thinking, connecting two things that have no actual or logical connection, as well as correlation implies causation.