It means that someone is extremely stupid that they don't have a functional brain, instead they have shit (meaning nothing) where their brain is supposed to be.
Person # 1: Where the hell is Ray?
Person # 2: I don't know, I don't think he's coming tonight.
Person # 1: He's such a fucking idiot, he's ruining it for me too, I swear he has shit for brains!"
A serious medical condition where fecal matter has replaced brain matter. Dangerous, but with low mortality rate.
Symptoms: Verbal diarrhea, poor decision making skills and acne.
Cure: There is no known cure, recommend quarantine from general populace.
Exhibit A: George W Bush - Ran up a big bill, couldn't find a WMD or Osama in 2 terms.
Exhibit B: Everyone who voted for him.
Exhibit C: Most politicians.
Usage: Your alcoholicdad has shit for brains, you are a credit to the family.