Also known as SP, Sanity Points are one of the most important stats in the Shadow Hearts series.
As the name implies SP is a measure of a character's sanity during battle. The SP varies for each character, some may have a naturally low amount while others will be rather high.
Narratively it's a reflection of the stresses of battling preternatural entities - with characters that have long experience of the supernatural (Yuri, Keith, Joachim, etc) having a higher base SP stat, than those who have had little such interaction (Alice, Karin, Johnny, etc).
Should SP reach 0 during battle, that person will go into the Berserk status. Under this status, characters will behave erratically and will possibly attack the allies of their own party.