Do not cause trouble in a place where you must be on a regular basis. Often used with workplace romances but can also apply to relationships with students at your school or starting shit in general.
Kyle tried to ask Jennifer out. I told him don't shit where you eat.
This phrase means "do not have romantic relationships with any co-workers." Basically, you don't want to make yourself uncomfortable (by potentially having a romantic relationship get ugly, or "shitting") at the place where you work ("where you eat").
Dude #1: "damn a really hot blonde just started working at my company. i'm gonna ask her out"
Dude #2: "dude, haven't you heard the saying: Don't shit where you eat?"
This expression refers to doing anything that would jeopardize something important or essential to you. A common example of shitting where one eats is engaging in a romantic affair with a co-worker, but lying to your roommate or stealing from friends also fits this expression.
Local Bike Shop Mechanic #1: "Can you believe that guy? I've hooked him up dozens of times, but after the tantrum he just threw, I'll never take a dime off a part for him again."
LBS Mechanic #2: "Seriously. Hasn't he ever heard? Don't shit where you eat."