Collectibles are special objects that you can photograph and use as decorations in your HQ - The Church. You will be able to do this after completing the mission "Office Décor". A total of 115 such objects are available in the game, 86 of which can be photographed and another 29 you will receive as rewards when completing missions, finding all discoveries of a given type, completing criminal ventures, etc.
When you obtain 85 items in the Collectibles app (both those photographed and those received as rewards count) the you will unlock "The Collector" achievement / trophy.
Collectibles are divided into 4 categories small, medium, large, and wall. What may be confusing is that sometimes the size of the object you have to photograph does not directly reflect which category it will end up in. For example, a huge sign photographed may go into the medium category, etc.
