Both chicken feathers and garlic skin are the rubbish left when cooking a chicken. Being worthless, they attract little attention. The Chinese use the expression chicken feathers and garlic skin to describe something unimportant or worthless, which usually does not merit people's attention. Sometimes the phrase also refers to something very boring or trivial.

Examples
① A: He doesn't seem very happy these days. When he sees me he doesn't even say hello to me.

B: Well, don't take offence at such a trivial matter.
② A: The young married couple often quarrel over which dress to wear and which dish to eat.

B: It is stupid to quarrel over such trivial matters.

鸡的羽毛、蒜的外皮儿都是做饭剩下的垃圾,不是什么贵重的东西,引不起人们的注意。汉语里用"鸡毛蒜皮"来比喻不重要的、没有意义的小事,通常不值得人们注意或计较,有时也用来指无聊的事。
例句
① A：最近他好像不太高兴,见了面也不和我打招呼。 B：咳,别去计较那些鸡毛蒜皮的小事。
② A：他们小两口经常因为穿什么衣服出门、吃什么饭吵架。 B：为这些鸡毛蒜皮的事儿吵架真不值得。