Saves (or "saving throws") represent your character's ability to resist or mitigate negative effects. There are three separate saves: physical, mental and spell. Which one is used depends on the type of effect you're being hit by.
Saves are compared against one of the attacker's derived stats: physical power, mindpower or spellpower, depending on the talent the attacker is using. Note: this is not the same as "depending on the type of effect". The comparison is not always physical vs. physical, or mental vs. mental, or spell vs. spell. For example, a spell that inflicts confusion would match the attacker's spellpower against the defender's mental save, while a psionic talent that inflicts confusion would match mindpower vs. mental save.
If the defender fails to save against the effect, but the defender's save is higher than the attacker's power stat, then the duration of the effect will be reduced. On the other hand, if the attacker's power is in a higher tier than the defender's save, the defender will suffer an additional cross-tier effect.
Saves are rescaled stats with diminishing returns. Equipment that gives +10 physical save may actually increase the effective save by less than 10 points, depending on which tier the save is currently in.