A True Alpha is a werewolf who becomes an Alpha by strength of character and will. True Alphas are rare.
A werewolf cannot become 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 that a werewolf can't steal a True Alpha's power by killing them.
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.