A person who has a motorbreath is someone who drinks so much alcohol that he could drive a car with just his breath. So motorbreath is a word that explaining how your breath smells booze.
When Metallica played this song before releasing their first album, their guitarist back then (Dave Mustaine) told about the meaning behind the song - which was about drinking and that's the way Metallica lived back in the 80's.
"Motorbreath is how I live my life!" - Metallica - Motorbreath
"Dude... how much have you been drinking?!"
"Not that much man..."
"You kidding me? You got motorbreath bro, don't try to fool me".