Special abilities are unique powers tied to a person's existence, and awakened in moments of need. Each ability has specific restrictions to it, and the only way to learn about them is to use it and experiment with it more. An example would be illusory types, who have an ability to resist illusions, and all kinds of illusions made themselves will disappear if the perceiver is aware that the illusion is an illusion. It seems that there are different categories of abilities, tied to bloodline, from healing-type to illusory-type. All abilities have their uses, you just need to get creative.
An awakening is the event that triggers the manifestation of a person's ability. Typically, it consists of a moment of strong emotion that plays a key part in determining the nature of the ability. Often, an Awakening may manifest at a young age, usually during a pivotal moment of an individual's life.
It seems that it is possible be unable to awaken an ability, according to Five. It can happen to everyone, but they don't all suffer from it to the same degrees. In general it causes them a lot of problems to be born unable to awaken an ability, but some races are more affected than others.
Humans cannot awaken more than one ability. For this, they are much weaker than the other races, and they are forced to make up for it with man-made weaponry. Known human abilities include a way to detect when others are using abilities, healing touch, illusory disguise, imbuing food with healing energy, and barrier creation.
A group of humans, called the Umbra, have abilities unique to their bloodline that are not present in other humans and races.
Monsters, like humans, cannot awaken more than one ability, but they are able to push it to further lengths and recover faster than any races afterwards. Known monster abilities include healing flora, control over fire, and possibly manipulating a person's lifespan.
The winged's abilities tend to be more abstract in nature than the other races, allowing them to technically harbor more than one ability. Known winged abilities include good fortune, as seen in Meimona.
In rare cases, once an individual has attained complete mastery of their ability, they may enter a state known as the Resonance. In this state, an individual's body and soul become perfectly synchronised, presumably allowing an individual a more dynamic use of their ability.
Very few individuals are able to achieve the Resonance within their lifetime, as the extent of mastery needed to do so requires years of intensive training. Captain Lune is noted to have mastered the Resonance at a relatively young age, though this is largely attributed to the harsh upbringing subjected to members of the Umbra Clan.