“Finger-lickin’ good” generally refers to especially tasty food.
Example of use: Ruth—”Mom’s pasta was so delicious that I had three bowls of it , Roger—”I know, it was finger-lickin’ good”.
The origin of the phrase “finger lickin’ good” is one that’s familiar to people in Western nations where the restaurant Kentucky Fried Chicken (KFC) is popular. The phrase has been among the company’s top advertising slogans since it was founded by Harland David Sanders (also known as Colonel Sanders) in 1932. Recently, KFC decided to abandon this slogan, and announced that its new catchphrase will be "So Good". The reason for this change, was in order to boost KFC's image as a more health conscious franchisee.