This gives you a quicker start in Multiplayer. You need them to craft 'Star Cards' in Multiplayer mode, which are basically your perks/skills and normally are very time consuming to obtain. Obtaining all collectibles is the quickest way to earn crafting parts. They are all found on your path to the main objectives.
Only 7 contain collectibles out of the 13 missions. You do not have to collect them again if you die or quit out to the main menu after collecting them. After finding a collectible, it is instantly saved. You can get them at any time using mission select. There is one milestone per mission collectibles. In the campaign milestones, press Triangle to get the crafting parts. You can collect the crafting parts by going to the Career screen at the main menu. Search the indicated locations to find all 23 collectible in the campaign and get 175 crafting parts for Multiplayer mode (25 crafting parts per mission).