"Gain an extra +100 Health on each respawn if you don't get a kill or touch the flag, up to +300 health. Suicides negate this effect."
Determination takes pity on the players that have trouble getting a kill without dying, and gives them extra health to try to help them out. If you suicide, you lose the extra health. This is a Secondary Perk and is free.
This perk helps flagrunners, whose only goal is to grab the flag and not get kills.