Kwamis are sprite-like, "abstract" creatures that give power to people with Miraculouses to transform into animal-themed super beings.
As explained by Master Fu, Wayzz, and Tikki in the second issue of Miraculous Adventures, kwamis are formed whenever a new abstract idea or emotion comes into existence in the universe, such as creation, love, beauty, and mathematics. When these emotions came into being, kwamis were formed at different times, such as Tikki, the kwami of creation, who was formed at the beginning of the universe and was the first kwami (and being) to exist. However, the kwamis couldn't be spotted by regular tangible creatures like humans. While they were able to journey across the universe, kwamis weren't sensed by humans and were unable to interact with them.
The issue was solved thousands of years ago, when a mage figured out how to create magical jewels, Miraculouses, in order for the kwamis to be able to communicate with and assist people. From that point on, kwamis helped the wearers of their Miraculouses achieve good in the world, although there were instances where they stuck with villainous holders and forced to help them with their diabolical schemes.
Generally, kwamis are small, being around 10 centimeters in height, with large heads and tiny bodies. They have arms and legs, but they lack fingers and toes. The animal theme that their Miraculous has affects their appearances, such as Tikki being red with black spots and antennae like a ladybug and Plagg being black with green eyes, cat-like ears, and a cat-like tail.
Normally, kwamis can fly and levitate. They can also become intangible to pass through solid objects, like locker doors. Even though they are small, kwamis appear to have enough strength to hold things that are larger and/or heavier than themselves. They can live for thousands of years — possibly forever — having been around since the creation of the Miraculouses.
Kwamis inhabit pieces of Miraculous jewelry, like earrings or a ring, in order to give the person wearing them the ability to transform into superheroes and gain a specific power, such as Plagg granting the power of destruction and Tikki the power of creation. The transformation can last indefinitely unless the Miraculous' special power (e.g. Ladybug's Lucky Charm or Cat Noir's Cataclysm) is used, at which point the wearer has about five minutes until they revert to their normal form and the kwami leaves the Miraculous. To regain power, to strengthen themselves and to transform their wearer again, kwamis need to refuel by eating food. Some kwamis have a preference for specific foods: for instance, Plagg's favorite food is Camembert cheese, but he is willing to eat other types of cheese if Camembert isn't available for him.
Tikki reveals that she is more than 5,000 years old in "The Pharaoh", suggesting that kwamis are immortal.
Kwamis are aware of the actions of the people who possess their Miraculous when transformed.
However, they cannot communicate with their holders when they are transformed.
An example of this is when Plagg laughed at how Adrien said all the rude things to Ladybug when he was possessed by Dark Cupid's arrow as Cat Noir in the episode of the same name.
In "Ladybug & Cat Noir", Tikki and Plagg appear to be unaware whether the akuma was captured or not, so it is actually unsure to what extent they can be aware what is happening when their Miraculous is used.
Kwamis are like Aladdin's genie, having to obey their holders' desires.
They are not, however, genies. Genies exist in universe, according to Plagg in "Ladybug & Cat Noir".
Kwamis can get sick, as seen in the episode "Princess Fragrance" when Tikki becomes sick after helping Marinette defeat a villain in pouring rain.
Master Fu is able to heal them.
As revealed in "Ladybug and Cat Noir", when the current holder disposes of their Miraculous, the associated kwami disappears and goes back into the dormant Miraculous. When the Miraculous gets put on again, whether by the same user or a new one, the kwami comes out of the Miraculous.
If the Miraculous comes off by accident, like when Adrien's ring falls off in "Lady Wifi", the kwami is not pulled back into the Miraculous. The kwami will only disappear if the holder wants to get rid of the Miraculous.
It is unknown if kwamis can be akumatized, but Season 2 will have the answers, as revealed at the Miraculous Ladybug panel at SDCC 2016.
According to Jeremy Zag, Season 2 will include an episode revealing the origins of the kwamis.
The New York Comic Con 2016 panel additionally noted that there will be webisodes that focus on the kwamis, notably Tikki and Plagg, and that there may be more than one episode in new seasons that centers on them.
The official Miraculous Ladybug Twitter account noted that while more kwamis will be seen in Season 2, it won't be all of them.
A teaser trailer released on August 31, 2017, revealed that some of these new kwamis are based on the animals of the Chinese Zodiac, yet the rabbit was not included or confirmed.