An illusory correlation occurs when an individual imagines that a correlational relationship exists between data sets (usually with people, events, or behavior) when it really doesn't.
An example of this could be looking at the relationship between washing your car and rainstorms. We all know intellectually that washing your car has no real effect on the frequency of rainstorms but it frequently seems that it rains shortly after washing your car. This may seem as if it is correlated but this is most likely because we are better able to recall those times when it rains on our clean car because we get frustrated and take note of the situation. We are less likely to remember the times we wash our car and it doesn't rain - this situation is less memorable and less likely to stand out in our memory.