feather在这里是用做动词，意思是“用羽毛做”，nest就是鸟巢。to feather one's own nest就是用羽毛来铺垫自己的巢，引申为假公济私，中饱私囊。

【例句】
He went into illegal business to feather his own nest.
他做非法生意以达到假公济私之目的。

They are always trying to feather their nest.
他们总是想尽办法中饱私囊。