The most embarrassing thing happened to me yesterday at lunch. My problems started in the morning. I forgot to set my alarm and woke up late, so had to rush out of the house without breakfast. By lunchtime, I was so hungry! I scarfed down my lunch like I hadn't eaten in days! The embarrassing part was that my very cute coworker saw the whole thing and I didn't notice until I was finished! Now he probably thinks I always eat like an animal. So embarrassing.
This week's party will include a formal dinner. Please use appropriate language. Please do not scarf down your food and don't forget to put your napkins in your laps.
to scarf down something means to eat something very quickly without regard for manners. When using this expression, a noun or name of food should follow the expression.
He scarfed down the whole bag of potato chips by himself.
Don't scarf down your dinner. You'll upset your stomach.
In Example 1, the speaker is recalling the embarrassing experience of being extremely hungry and so eating her food so quickly and ravenously. At lunchtime, she didn't care how she ate, or how she looked while she ate because she was very hungry. Only after, she realized that someone else had witnessed her wild eating.
In Example 2, the speaker is giving instructions for the upcoming party. Since the dinner will be formal, participants are instructed to eat slowly and politely, NOT to scarf down their food.