SHANGHAI—China's legislature on Saturday formally eased two restrictive social policies of its authoritarian system, allowing some couples to have a second child and ending a form of extralegal detention.

The standing committee of the National People's Congress approved the relaxation of the 1980s-era one-child policy by allowing more couples to have a second child, in particular certain families where one parent was an only child. The legislature also decided to end a form of detention called laojiao that allows police to...