This might sound like a mouthful in Latin, but in English it's pretty simple: Correlation does not imply causation. Just because two events often occur together, one does not necessarily influence the other. For example, you'd be relying on this fallacy if you were to say: "There is a correlation between the cost of the damage of a house fire and the number of firefighters who show up to fight the fire. Therefore, many firefighters cause much damage."
You can see, with an example like this, that it's unreasonable to assign the cause to the firefighters. The only reason for a correlation between firefighters and damage is that both of these numbers rise with a larger fire.
Another example: Murder rates and ice cream sales rise in the summer. But that doesn't mean you can logically conclude that ice cream makes people prone to being murdered.
Directly translated, this Latin phrase means "After this, therefore because of this." This fallacy implies that because one event always follows another event, the first event causes the second. Examples of this occur in ballparks across America. It is the thinking that "Every time I turn my hat inside out the batter swings and misses, therefore, turning my hat inside out causes the batter to miss." The batter is not actually influenced by the "lucky rally cap."
Confirmation bias is to inductively seek information that supports a presumed outcome and to ignore information that challenges the bias. This logical fallacy is frequently employed by those seeking to confirm the supernatural. For instance, person attempting to investigate paranormal phenomena might say that audio imprints of ghosts can be faintly heard on an audio tape. Playing back the tape -- which is bound to contain some faint sounds -- and then claiming proof of ghosts is confirmation bias. A ghost was not the cause of the noise; the noise was the cause of suspecting a ghost.
This fallacy is nicknamed the Texas-sharpshooter fallacy, based on a joke: A Texan sprays bullets across the side of a barn. Where there is the highest concentration of hits, he paints a target and announces that he is a sharpshooter. This fallacy is frequently employed by those looking to prove prophecies and predictions. They point first to the result and then apply a vague "prophecy" that matches it.
Gamblers who believe they are due for a win should beware. They're committing the gambler's fallacy. Implying that, for instance, a coin must come up tails, statistically, just because it's come up heads the last 10 flips is an incorrect assessment of the way statistics cause an effect. The coin has a 50-50 chance on each flip, not on a series of flips. Likewise, assuming that a roulette wheel is likely to land on red, based on its previous black lands, is equally fallacious. In games of chance, past outcomes do not effect future results.