To avoid drawing attention to yourself, staying out of trouble, by keeping a low profile, avoiding confrontation with (black) people, not driving a car or wearing clothes that draw attention. Especially used by people of color who can easily get into trouble, especially when they decide to "keep it real"
Jerome: hey dawg why ain't you sayin' anything to Shakalika and her boyfriend Andre?
Jamal: I stayin' out of trouble dawwwg, I keep it low
Jerome: I keeps it low too!
Quentin: boss, watcha doin'?
Germaine: Just nuttin, I keeps it low
Quentin: Dat's gooood!