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?"