Per capita distribution means "per head" in Latin and each descendant takes an equal share. If, for example, one sibling and two nieces of a deceased sibling are the right heirs, each would get one-third of the estate.
Per stirpes distribution means "by the root" in Latin and each descendant takes a share determined by the root--or what that person's deceased ancestor would have inherited. For example, if a child would have inherited one-half of a decedent's assets, but died first and left three children, those three children would each inherit one-sixth of the estate (each would inherit one-third of their parent's one-half share).