Presents are important items that the Evil Acorn stole from Conker at his birthday. They come in blue and red variety and have yellow ribbron strings. When the Evil Acorn kidnapped Berri, he also stole the presents with him and he scattered them along the world when he ran away. B&R presents (along with Invitations) are required to access the locked doors of The Mysterious Cave, where there are more red presents and goodies are to be found in. They are also required to fully complete the entire game.
Blue Presents are very important to Conker's journey through the worlds, as he cannot exit the world he is in until he collects all the blue presents of that world. Blue Presents are found by completing puzzles, accessing areas with items and defeating bosses and playing mini games. There is a total of eight to find in each level.
Red Presents are highly different from blue presents, they are optional to collect, however they can be difficult to collect as some cannot be accessed until you revisit a previous world with another item from a different world. Red presents (and invitations) are required if the player wishes to fully complete the game 100%.