Everybody has an aura. However, the only person that this is important to is Leena, as she is the one able to sense auras. In general, she can sense one's mental and emotional state, including Claudia's bouts of darkness, Artie's endless nerves and especially Pete, whom she is initially quite attracted to.
A more interesting feature of auras, and one that foreshadows one of the more remarkable revelations of season 4, is that they also exist in Artifacts. Leena is able to directly sense where an artifact is safest and directs Artie towards those locations. Without her, a very involved ritual in a special room of the Warehouse is required to decipher the proper resting place.
Some rare humans have an Aura described in the Pilot episode as "In Tune". The only person described as such in the entire series is Pete, which makes it reasonable to assume that his Vibes are a result of it, and that his mother Jane shares the condition just as she shares the Vibes.