A True Alpha is a werewolf who becomes an Alpha solely by strength of character and will. True Alphas are rare, only appearing once in a 100 years.
A werewolf cannot be a True Alpha if they ever take a life as discussed by Scott and Ms. Morrell in The Girl Who Knew Too Much. In Smoke and Mirrors, Peter relays a True Alpha's status cannot be stolen were they be slain as in the manner of a regular Alpha.
During Season 3, Scott's eyes, in a number of situations of high duress and immense determination, briefly turn Alpha red. In Currents, Deaton confirms Scott has the potential to be a True Alpha. In Lunar Ellipse, Scott fully attains the status of Alpha by determinedly pushing through a mountain ash barrier, breaking it, fully awakening his True Alpha status.