Aura is an ability that everything with a soul can use with practice but it is originally locked. It can be unlocked through experiences that the body realizes that they need the aura to survive or someone can unlock it with their own aura. Because it is based on the soul, it can appear different for different people via color. Someone could be blue, another can be green, red, cyan, gray, etc. Since it is anything with a soul, Humans, Faunus, and the normal animals have it, leaving the Grimm as the only ones without it.
It can be used to project a barrier to prevent harm to the user [they can still feel pain and sensations similar to burning], shockwaves, unlock someone's aura, it automatically heals minor wounds [cut, bruises, etc], protect against the climate [winter, heat].
Those skilled enough can receive a 'warning' telling the user something is near as if they are being watched or stalked, feel other auras, and even identify someone based on their aura alone. However, the last two are high-leveled techniques and require someone to train in them for years.
Aura is also the main way to activate Dust and Aura can be used through weapons as a conduit.
However, just like more things, there is a limit to the amount of aura someone has and that it can be drained either over time or from an attack.
Now, aura is also connected to someone's Semblance.
A semblance is a unique ability every person with aura has access to. The best comparative would be the X-Men where they each have their own abilities but some people's abilities can be closely-related even when said people are not related by blood.
Semblances are powered by aura, therefore, semblances can not be activated if they have run out of aura. If they run out of aura, an easy way of telling is if their wounds are not closing.
While most Semblances are active [meaning they must activate through their own accord], it is possible to have a passive semblance [meaning it is active at all times].
Semblances can be improved similar to a muscle. They can also be modified by Dust. An example would be the ability to produce a clone to take your place. If they used Dust, the clone would take on the properties of the dust [explode, turn solid, freeze, etc].
However, just like a muscle, if an active semblance is used too much in a short time, it can make the user feel exhausted. The user's emotions could also affect the semblance either positively or negatively.