This is a man who'll put his dick in any and all types of pussy. He sleeps around excessively with many different females and probably has suffered from at least 1 STD in his life....therefore, making his dick "trash". The cool term for this is playa but to females a trash dick is just a triflin slutty man.
"Girl, that's why I don't date entertainers or athletes--because most of them ain't nothin but trash dick."
She broke up with her man because she found out what a trash dick he is.