Peculium means any property or asset assigned by the father of the family to a family member or a slave. The father of the family maintains the property right by the beneficiary will have the disposition right.
Let us note that, in Roman Law, onlay father of a family (Pater Familias) had the capacity to own and gain properties. Any property/asset held or gained by the family members or slaves would be the father's property. Accordingly, members and slaves could have anything to dispose only by provision of peculium.
Let us also note that this term is the origin of today's English phrase "peculiar to". Where a property is provided as a peculium to someone, that property is 'peculiar to' him or her as it was assigned exclusively by the father.