If you use death prism on a mob, the next time that mob takes death damage, the damage will be converted to life damage instead. For example, if you're fighting a rank 4 non-boss death mob, it will usually have +30% death resistance and -30% life resistance. If you use vampire without death prism, instead of 350 damage, the 30% death resistance makes it only 245 damage. If you use death prism first and then vampire, the -30% life resistance makes vampire do 455 damage instead.
Prisms become more important as you get higher level, both because mobs get stronger resistances and vulnerabilities, and also because you do more damage in a single blow with higher pip spells.