We use mind share to mean the number of people who have adopted a particular cultural variant or Meme in theories of Darwinian Cultural Evolution. In genetic evolution, a genetic variant maximizes its fitness by increasing the number of descendents having that variant (Inclusive fitness), whereas a cultural variant maximizes its fitness by increasing its appeal. This may be an intrinsic appeal of the variant (like a catchy tune), but most often the appeal is context dependent. With Prestige Bias we choose a behavior or belief because it is favored prestigious early adopters. As a variant becomes common, Conformity Bias becomes important.
A similar previous use is from marketing, see Mind share.