The targeted customer groups can be high or average income; especially the latter can be premium-aware but on the lookout for bargains.
Premium brands are designed to convey an impression of exclusiveness or rarity, especially in the mass markets. Frequently, companies will invent different (sub)brands to differentiate their product lines into a premium and a general segment (e.g. Toyota with their Lexus, Prius, and Scion marques). In most ways, the premium segment can be thought of as the contrary or a complement of value brands. The success of a brand is determined by the combination of aforesaid category and the market share. In that sense, the term "premium" replaces the traditional attribute "luxury" although the former can be perceived as less ostentatious.
^"Exclusive, rare, limited, or premium?". thehipperelement.com. 2014. If you have an unlimited supply, everybody knows that lots of people are using it, and there are no restrictions, that means it’s not exclusive, not rare, and not limited. ... “Premium” is an artificial limit on something that is not actually limited, aimed at people who have higher expectations, and therefore a higher perception of value.