Per stirpes is a legal/financial term used to indicate how an inheritance should be distributed. It means that the inheritance should be split equally by each member of a group sharing a certain kinship with the deceased (usually the deceased's children). If one of the group has died, but has left offspring, then that person's share of the inheritance is split between his or her offspring.
This is in contrast to per capita, in which each person (including the offspring of the dead heir) are given an equal share.
From the Latin for 'through the roots'.
An illustrative example
Zack has two children, Adam and Chris. Adam has no children. Chris has two children. Zack and Chris die in a violent fishing accident. It was a quick and painless death.
If Zack's will says that his money is to be distributed per stirpes, Adam gets 1/2 and Chris's children each get 1/4.
If Zack's will says that his money is to be distributed per capita, Adam gets 1/3, and each of Chris's children get 1/3.