A catalogue, in ACNL, is the little machine you can go into in the Nookling store (you need to upgrade it from Nookling Junction to T&T Mart to unlock the catalogue) and it is, basically, an ongoing list/database of every item you have collected in the game.
To upgrade Nookling Junction to T&T Mart, you have to:
Spend 10,000 bells towards your house mortgage,
Spend 12,000 bells on items in the Nookling Junction store,
Have had your town for 10 days.
Anyways, the catalogue gives you the opportunity to go back and re-order any items you have previously collected (in case you need duplicates or you have gotten rid of an item that you want back). All items are sold on this catalogue for the same price as if you were to buy them in the store normally. You cannot re-order non-orderable items. For example:
fortune cookie items,
DLC items,
Mannequins,
Hybrid Flowers,
Usables,
Golden Tools,
etc.
When you order an item from this catalogue, it will be sent via the postal system in Animal Crossing to your player. We use this cataloguing system as we trade, as any item your ACNL character picks up is now in your character's catalogue, and you can order it again. If you catalogue an entire series of furniture, you can then order that entire series of furniture as many times as you would like to!
