Quote from Silmarillion:
I know the desire of your minds that what ye have seen should verily be, not only in your thought, but even as ye yourselves are, and yet other. Therefore I say: Eä! Let these things Be! And I will send forth into the Void the Flame Imperishable, and it shall be at the heart of the World, and the World shall Be; and those of you that will may go down into it. And suddenly the Ainur saw afar off a light, as it were a cloud with a living heart of flame; and they knew that this was no vision only, but that Ilúvatar had made a new thing: Eä, the World that Is.
Thus it came to pass that of the Ainur some abode still with Ilúvatar beyond the confines of the World; but others, and among them many of the greatest and most fair, took the leave of Ilúvatar and descended into it. But this condition Ilúvatar made, or it is the necessity of their love, that their power should thenceforward be contained and bounded in the World, to be within it for ever, until it is complete, so that they are its life and it is theirs. And therefore they are named the Valar, the Powers of the World.
What does necessity mean in this phrase?
Does it mean that Ilúvatar needs the love of them, or that this condition is like a proof to them? So, if they do this condition, it proves that they love him.