It's often used in situations where someone is:
* Strongly disagreeing with something: "Je ne mangerai jamais de la vie ce plat!" (I would never in my life eat that dish!)
* Refusing to do something: "Je ne lui pardonnerai jamais de la vie!" (I will never in my life forgive him!)
* Expressing a strong opinion: "Je ne crois jamais de la vie à ce qu'il dit." (I would never in my life believe what he's saying.)
Essentially, it's a more forceful way of saying "never" in French.