Purchase is Tressa's Path Action in Octopath Traveler. This ability allows Tressa to obtain special items from townsfolk. This includes items not sold in stores as well as items that might come in useful. This Path Action is the noble counterpart to Therion's Path Action, Steal. The items obtainable from both Purchase and Steal are the same.
Regular items can generally be purchased cheaper this way than from stores, though in more limited supply. Also, unlike other noble Path Actions, Purchase isn't limited by your character's level but instead by how much money you have.