"post-hoc" refers to analyses that are decided upon after the data has been collected, as opposed to "a priori".
"post-hoc" refers to analyses that are decided upon after the data has been collected, as opposed to "a priori". The more the data is examined post-hoc and the more statistical tests are run on it, this should be taken into account by multiple-testing procedures.
It is also a (outdated) concept of causality "post hoc ergo propter hoc" (meaning "after this, therefore because of this"). The idea is that if we always observe event $Y$ after event $X$, $X$ must have caused $Y$. This concept underlies for instance the Granger causality test. Nowadays this post hoc notion of causality is not accepted as actual causality.
