What does "The Quality of Mercy is not Strained" mean?

I think I know what Shakespeare meant for Portia to be saying when he wrote this dialog between Shylock and Portia, and I found a decent discussion on the web here.

What I want to know is, what do people mean, when they quote this figure-of-speech by itself. It seems to have acquired a meaning of its own, a proverb that in the end, embodies some meaning which maybe is supposed to be clear to everybody, but which is not clear to me.

Is it used by those who quote it, for example, meant as a rejoinder or insult against someone who seems stubborn, recalcitrant, and uninterested in the mores of the larger society? Has anyone seen a cataloging of other places in literature where this quote is used, or is the quote largely used in conversation only?

"Strained" is a Shakesperean-era term for "forced or constrained"; it means mercy must be freely given. You can grasp this by seeing the quote in context:

The quality of mercy is not strain'd,
It droppeth as the gentle rain from heaven
Upon the place beneath. It is twice blest:
It blesseth him that gives and him that takes.

Portia is importuning Shylock to show mercy, but recognizing that she cannot demand it. Shylock declines, of course, and this proves his undoing, for now Portia uses his "letter of the law" attitude against him.

A modern-day equivalent would be something like

Look, I can't force you to give me a break here, but it would benefit us both if you did.

I think the situation where this quotation is most commonly used today is rather the obverse of Portia's plea. She was asking for mercy but making the rather obvious point that she could not force the plantiff to grant it. (Strained here meaning forced). The usual context today, I believe, is to refute another persons claim to have behaved mercifully or generously by pointing out that they actually had no choice other than to do as they did. Example:

Well, I gave two thousand pounds to charity last year.
Only because your accountant told you to pay it to avoid surtax. TQOMINS.