What is the "Cause" of the Oppressed?

Social justice Christians will often bring up the observation that there are a number of passages in Scripture that command God’s people to take up the cause of the poor, the oppressed, the fatherless, the widow, and the foreigner. But what exactly is this “cause” that God wants His people to take up? And, as God’s New Covenant people, how can we do that in our own modern context?