"minchia" means "cock" (not penis) in sicilian dialect even if well understood and partially used in the rest of italy, expecially south-side. Alltought when it's used in the north of Italy or in the rest of the world it gives a "sicilian" connotation to the sentence.
It's a female noun (in italian every noun has a genre) but it's not the only example of italian that words describing genital organs while having the opposite grammatical genre.
General use, apart the litteral one, is - as for "cazzo" - to get sentence stronger as in english is done with fuck.
Used in the form "...sta minchia di..." (this minchia of)
means something not worth or definitively shitty or actually boring
The variation "Minchione" (literally "big minchia") is used to refer to somebody really dumb
"Tengo una minchia tanta" (this sentence is part of a Frank Zappa's song singed in italian)
"I've got a huge minchia"
"what the fuck you want?!"
"che minchia vuoi?!"
"suca la minchia, scemo"
"this minchia of car wont never go again"
"Sei proprio un minchione"
"You're truly dumb"