If you like to maintain a massive stockpile of nuclear weapons, you'll love this policy. It cuts their maintenance cost in half, allowing you to wait for the right moment to unleash nuclear hell on your enemies without having to worry as much about your empire's economy.
The first strike in a nuclear exchange is the initial salvo. A second strike is the ability to destroy a nuclear attacker with a retaliatory attack, even if the initial attack (the first strike) results in the destruction of the second striker. It is, in summary, a way to strike beyond the grave. In the cold, inhuman, rational calculus of nuclear deterrence theory, a second strike capability ensures that the nation will not be destroyed by an overwhelming first strike.