From the mouth, the bolus (chewed ball of food) passes through the pharynx (throat) and into the esophagus.
The epiglottis prevents food and drink from entering the trachea (windpipe). (see animation below!)
The esophagus is a thin, muscular tube that brings food to the stomach.
Food does NOT just "fall down the esophagus" by gravity- it is PUSHED through the digestive system by muscular contractions called peristalsis!
This means that you can swallow food upside down- it would still make its way to the stomach by peristalsis.
Epiglottis- In the first animation, you can see the epiglottis- a protective flap that prevents food from getting into the windpipe when food/liquid is swallowed.