The nuclear option, in a colloquial sense, is the most extreme solution to a given problem. The term dates back to the 1960s, where it arose in the wake of the Cuban Missile Crisis. It was originally used in reference to actual nuclear weapons. Less extreme solutions are sometimes referred to as non-nuclear options.
Some examples of how the term nuclear options is used:
When Microsoft and Dell had a conflict some years back, there was some speculation that Microsoft might go for the nuclear option of no longer allowing Dell to ship MS operating systems.
Since 2003, nuclear option has also been used to refer to a parliamentary procedure in the United States that allows a simple majority of votes to determine that debate on an issue will end and voting can proceed. Another use of the term is in reference to choosing nuclear power plants to generate energy rather than other technologies.