"Post hoc" is a short version of the Latin phrase that translates to "after this, therefore because of this." A common use of the term is defining "coincidental correlation," assuming because an event happens after another the first event caused the second.
An example of the basic logical flow of post hoc analysis is: An earthquake occured and then Jim's house crumbled; therefore, the earthquake must have caused Jim's house to crumble.
The fallacy of post hoc analysis is that an order of events must cause events to occur. It is not always true, however, that the first event caused the second. For example, Jim's house could be termite-ridden, weakening the structure and influencing the house's crumbling after the earthquake.