Digestion is parasympathetic nervous system dominant process and hence is most stimulated when you are most relaxed. You will digest more efficiently during sleep as your parasympathetic nervous system is dominant at rest which favours blood flow through your enteric bloodstream which enhances absorption of gut breakdown products. Parasympathetic activation also stimulates salivary gland secretion, gastric activity and peristalsis.
ETA: Also the reason why you get sleepy after eating. Blood is diverted towards digestion, therefor making you tired.
While no scientific evidence points to particular health problems associated with sleeping after eating, doing so may be problematic for some people.