Definition of Dōjinshi?

I don't exactly understand the definition of a Dōjinshi, I looked on Wikipedia but that just complicates the answer. Is it a fan manga? kind of like PowerPuff Girls Dōjinshi or Grim Tales by Bleedman, his are fan comics and he calls them dōjinshi. I understand they don't have to be anime , but is a fan manga based on a real published manga count as a dōjinshi? What's the exact, a bit simplified definition.