moral obligation

Lately I keep on hearing the term 'moral obligation'. For example "James Hardie has a moral obligation to pay asbestos victims."
My question is this. What is the basis for talking about a moral obligation?
Does it mean 'the majority'? In that case moral obligation changes depending on the feeling and knowledge of the electorate.
Does it mean 'feeling'? That is I feel they have an obligation.
Or is it based on something more substantial?
One of the reasons I am a follower of Jesus is precisely because I then have a rationale for life decisions. Respect others because God created them and loves them, not because I have a 'moral obligation'.
Francis Schaeffer once said something like this. (I paraphase in my words.) "All we need to do is to push people to the logical conclusion of their belief system and they will discover either despair or embark on a seeking journey towards God."