Most items from the Store are character-bound which means they only belong to your character who purchases the product, and not all of the characters on your account. Some products like all Tournament outfits and Tournament mounts are account-bound which means they apply to all the characters on your account, not just one. With that being said, some items that are not from the Store are also character-bound, for example, all rewards from the Hunting task. If you're curious to know about other items are attached to just one character I recommend you visit this related question: What type of items are character bounded?
When an item is attached to just one character it goes to that one character's store inbox. These items are indestructible and no one will be able to steal or take these items, even if invited to your house. If you have to character-bound house items, you're only allowed to put it in the house you own on that specific character, no one else's even if it's a guildhall. Please note, you cannot trade these items or throw them outside of a house. If you must you can put them in your depot, leave them in your store inbox, or keep them in your house.