Hi, Chance.
It depends on what you bought, but most items are either clothing, furniture, collection helpers or Karma Powers.
Clothing is available from the mirror and in CAS. Furniture ends up in the Buy/Build Mode catalog. Collection helpers are added to the Sim's inventory (or possibly the Family Inventory in Buy/Build Mode -- I'll have to check the guide), and Karma Powers unlock in the Karma Powers screen.
Flynn