In role-playing games such as Dungeons & Dragons, it is common to have the opportunity to deflect, decrease, avoid, or recover from certain types of attacks. You roll the specified dice, and if they come up with the required number or higher, you have saved yourself from some or all of the damage. The process of performing this is called "making your saving throw"; the number itself is also called your "save".
For example, suppose that your character has been knocked unconscious in battle, and the game master says that you need to roll a 12 or higher on 3 six-sided dice in order to regain consciousness. When you roll the dice, you get a 6, 4, and 3, totaling 13: this is higher than the 12 you needed, so you have "made your saving throw" and your character wakes up and can take actions again. If you had rolled 6,4,1 for a total of 11, you would have "failed your saving throw" and your character remains unconscious until the next opportunity to try to wake up.
So, the title is a reference to role-playing games and this damage-avoidance/recovery process; and the "throw" of "saving throw" refers to physically throwing dice to generate a random number.