Per Stirpes refers to a method of distributing property. Per Stirpes is defined by New York Estates Powers and Trusts Law §1-2.14 as:
A per stirpes disposition or distribution of property is made to persons who take as issue of a deceased ancestor in the following manner:
The property so passing is divided into as many equal shares as there are (i) surviving issue in the generation nearest to the deceased ancestor which contains one or more surviving issue and (ii) deceased issue in the same generation who left surviving issue, if any. Each surviving member in such nearest generation is allocated one share. The share of a deceased issue in such nearest generation who left surviving issue shall be distributed in the same manner to such issue.
For example: If your will distributes your property "in equal shares, per stirpes" and you had 3 children, your property would be divided in 3 equal shares. However, if one of your children died before you and that child had two children of his own, i.e. your grandchildren then your two surviving children would take one third and your two grand children would split their father's one third share.
A per stirpes distribution gives each child a equal share but after that first generation, the distribution can become unequal. To continue with the example above, if two of your children died before you, and that second child had three children, then those grandchildren would split the one third share, taking one ninth each. Their cousins would take one half of their father's share giving them a one sixth share.
Compare: By Representation and Per Capita