Literal Meaning
He begs to leave, like a hungry person who bids farewell without end
Implied Meaning
Although the hungry visitor constantly expresses a desire to leave, he wants the host to persuade him to stay for lunch and hopes that this will speed up the cooking process
Origin
It is unthinkable to host a visitor and fail to invite him for a meal. It is equally discourteous for a visitor to turn down an invitation to eat