The "nuclear option" refers to a political maneuver that would allow the US Senate majority (Republicans currently hold 55 out of 100 seats) to prevent the minority party (currently 44 Democrats) from filibustering judicial nominees, making it easier for the President's judicial nominees to be confirmed to the bench.

Short Answer: The Supreme Court, buddy.
New appointees will help decide, among many other things, whether Americans have a constitutional right to privacy, whether the federal government will be allowed to protect our air and water, and whether Americans can count on enforcement of laws that protect our civil rights. Many believe there will be an opening in the Supreme Court as early as June 2005, if Chief Justice Rehnquist decides to step down.

Short Answer: Say `Hello` to one party rule. Without the filibuster, Democrats would not be able to protect the courts against judges who would overturn decades of hard-won civil rights protections. This loss would also affect the minority voice on any future vacancy on the U.S. Supreme Court, which political pundits expect to happen in June, at the end of the current term.

Even more alarming is that the filibuster could be eliminated in other instances, particularly in the upcoming debate over the privatization of Social Security. The distinction between filibusters for judicial nominees and filibusters for legislation and other nominees has never been made before. Use of the "nuclear option" could very likely be a sign of the total elimination of the filibuster in the Senate.