Onion
The Onions are the nests of the Pikmin. Olimar named them so because of their resemblance to a vegetable native to his home planet. These bulbous plant-hives have brightly-colored bodies with a black-and-white band across the midsection. When landing they will land on some strange markings on the ground believed to be crop circles. How the markings are made and why pikmin onions land on them remains a mystery. Three stilt-like legs suspend the Onions out of the reach of hungry predators, and provide access to the inside for Pikmin. In Pikmin 1, Olimar states that he inspected the Onion's legs, and saw they were covered with tiny little hairs. There are three known types of Onion, each with unique coloration corresponding to either Red, Yellow or Blue Pikmin, and only one of each has ever been seen. Subterranean Pikmin species such as Purple Pikmin, White Pikmin and Bulbmin do not have Onions, or at least none that have yet been discovered.
During the daytime, Pikmin hunt and bring food, such as pellets or slain beasts, to the Onion, which in turn produces new Pikmin seeds. If there are fewer than 100 Pikmin on the field, the seeds are ejected and take root in the ground, but if not, they are stored inside the Onion, along with any other Pikmin not on the field. When night falls and all the Pikmin have returned, the Onion folds its legs and lifts off from the ground, presumably using its flower petals like rotor blades to propel itself into the low atmosphere, where it hovers until daybreak. If an Onion loses all its Pikmin, it will produce a single seed the following day to prevent extinction.
When the Onions were first discovered in Pikmin, they were dormant. They had a dark grayish color, were flowerless, and their legs were buried in the ground until Olimar came upon them, at which point they sprang to life and spat out a single seed. It is not known exactly what triggers this hibernation, though it's possible that a loss of Pikmin or food shortage may prompt the Onion to become dormant until conditions improve.
Types
Red Onion
The Red Onion is the first Onion to be discovered in both games. In Pikmin, the Red Onion is found at The Impact Site, dormant in the ground not far from where the S.S. Dolphin crashed. Once awakened, it will release a single Red Pikmin seed which Olimar can use to harvest nearby red Pellet Posies and spawn enough Pikmin to retrieve the Main Engine. In Pikmin 2, Louie finds this Onion in the Valley of Repose when he falls out of the Ship's cockpit and gets lost.
Yellow Onion
The second Onion the player will come across in both games. In Pikmin, it is found dormant in The Forest of Hope amidst several yellow Pellet Posies and free-standing yellow pellets. In Pikmin 2, the Yellow Onion is located in the Perplexing Pool behind a poison gate protected by a Fiery Bulblax, so White Pikmin and Red Pikmin are required to reach it. There are a few yellow Pellet Posies nearby which will not regrow once they've been harvested.
Blue Onion
In Pikmin, it can be found in The Forest Navel in a pool near the landing site, and is the third Onion the player discovers. Several blue Pellet Posies are in the immediate vicinity, as well as a free-standing blue 5 pellet. In Pikmin 2, the blue Onion is located in the Awakening Wood; although it can be seen relatively early in the game, it lies behind an electric gate, meaning that Yellow Pikmin from the Perplexing Pool are required to access it. A small pool blocks the only direct path up to the gate, so the Pikmin must be thrown onto a nearby ledge (while taking care not to disturb the Cloaking Burrow-nit lying in wait there). The Captain can then walk around through some water to reach them, and order them to defeat the beast and demolish the gate, allowing him to find the game's first 5 Blue Pikmin.
For some unknown reason, when landing on an area, the blue onion seems to hover a bit before landing, therefore landing slower than the Red Onion and Yellow Onion.
At the end of Pikmin, there is a rather confusing part where fourteen Onions, of colors that have not appeared in a Pikmin game so far, fly above the Planet of the Pikmin. It is unknown whether they are trying to follow Captain Olimar or merely hovering for the night. This could mean that more colors may yet be introduced in Pikmin 3. Interestingly, one of the Onions seen is purple, and Purple Pikmin were indeed introduced in Pikmin 2, but without an Onion.
In Super Smash Bros. Brawl
In Brawl, the 3 Onions appear as a trophy and on the "Distant Planet" stage. Here, when a pellet is thrown into one, an item is ejected. More items appear if the pellet and Onion have the same color, similar to the way it works in the Pikmin games.