Literally, it means "吃鹧鸪" but this phrase is usually used at the end of Fairytales as an ending line, similar to the English phrase: "they lived happily ever after".
Why "perdices"? I guess this animal was chosen because 1) it rhymes with "felices" 2) at that time, it was an expensive dish that only rich people could afford, which suggests that they never had any problem