The direct answer
Restaurant kitchen drains back up because grease and food debris accumulate faster than they drain. This happens in three main places: inside your grease trap (when it fills past 25% capacity), inside drain lines (when FOG hardens and narrows the pipe), and at floor drains (when the main trap is over-capacity and grease bypasses the baffle).
One backup is a symptom. Recurring backups signal that your grease trap service is not keeping up with your actual kitchen discharge — or your drain lines need hydro jetting to clear hardened FOG buildup.