Someone may be considered/accused of being 'thick as shit' for several reasons, mainly for thinking and acting in ways which most people would obviously recognise as wrong/stupid/flawed/absurd. Unlike people of higher intellect, such people will be unable to realise how hopelessly dumb they really are even after it has been clearly shown to them. These people are unable to understand simple logic and have very poor communication skills.
The term is typically used informally and is commonly used as an insult intended to cause offence.
"Ha Ha, you're thick as shit!"
"I know someone who ate cyanide because he's thick as shit"
"That person is obviously thick as shit"