Psik Reisha is a Talmudic expression meaning an inevitable consequence. Its main application is to the laws of Shabbat. To understand the concept requires a little background.
A permitted action on Shabbat that may possibly lead to a forbidden consequence is permitted. For example, it is ok to walk across grass on Shabbat, even though you might thereby inadvertently detach grass with your feet.
However, when the action will inevitably lead to a forbidden consequence, the same leniency does not apply; the action is forbidden. This situation is called a psik reisha, which means cutting the head in Aramaic. (Reisha is related to the Hebrew for head, rosh.)
The name comes from the Talmuds paradigmatic case of a psik reisha (Shabbat 103a). A man wants to cut the head off a chicken to provide a diverting toy for his child. (This was in the days before PlayStations.)
He has no intention of killing the chicken; to do so would be forbidden. (Slaughtering is one of the 39 categories of work that may not be done on Shabbat.) But can you cut the head off a chicken and the chicken wont die? asks the Talmud incredulously. Of course it will.
This is a clear example of an unintended consequence of an action that will inevitable transpire, hence the expression.