Literally, after this, an abbreviation of the Latin, post hoc ergo propter hoc (after this therefore because of this). The fallacy is based upon the mistaken notion that because one thing happens after another the first event was a cause of the second event. Many events follow sequential patterns without being causally related. For example, you drink fluids and two weeks later your cold goes away. You have a headache so you stand on your head and six hours later your headache goes away. You put acne medication on a pimple and three weeks later the pimple goes away. You perform some task exceptionally well after forgetting to bathe, so the next time you have to perform the same task you don't bathe. Many tribes have beat their drums during a solar eclipse to make the gods spit back the sun: it works every time! Simply because one thing happens after another does not establish that the two events are causally related.
You use your dowsing stick and then you find water. You imagine heads coming up on a coin toss and then heads comes up. You rub your lucky charm and then what you wish for comes true. You lose your lucky charm and you strike out six times. You have a "vision" that a body is going to be found near water or in a field and later a body is found near water or in a field. Your have a dream that Aunt Daisie's cow dies and then the cow dies. Etc. Etc. Co-incidences happen. It may be a necessary condition for an effect to come after a cause but it is not a sufficient condition to establish causality that one thing happen after another.
To establish the probability of a causal connection between two events controls must be established to rule out other factors such as chance or some unknown causal factor. For example, Quadro Corporation, makes and sells for $955 the QRS 250G "Detector" that is supposed to find drugs, arms, golf balls and almost anything else. To test the thing would be quite easy, but using it and finding some drugs or some golf balls would not count as proof. Testimonials from the corporation president would not count as proof. Anecdotes from some law enforcement officer, even if in uniform, don't count as proof. A controlled study, comparing success rates with true Detectors and fake ones, would count. Testing the device over a rigged field with buried drugs or golf balls placed there by an independent researcher would count. A testimonial from the Poopoo Police Department Captain that since they started using the QRS 250G their drug arrests have gone up 50% is worthless. Sequences don't establish a probability of causality any more than correlations do.