The Pri Ha'aretz teaches that every single absence that is noticeable in the world is an instance where the Shechinah was forced into exile. She is in exile in the lack. When we pray for her return to her rightful place, then all of that which is lacking in the world will collectively vanish with the restoration of her true status.
It's a difficult concept to picture, but it does illustrate the connection that is often made that we should pray for the well-being (completion) of the Shechinah, rather than for our own personal needs.
Still, I want to bring it down to a level that's a little more within our grasp. Even if it will be a very esoteric grasp, we'll try to get some kind of grasp on the abstract metaphysics of the issue.
The Shechinah, in a sense, represents the revelation of Godliness in the world. Godliness permeates all of existence, but in the default state of this world it is hidden from sight. Any revellation of Godliness is a manifestation we call the Shechinah.
[One question that arises here is that if we see two different people whose lives are both a revellation of Godliness, this doesn't imply there are two Shechinahs, rather the Tanya explains that it is like sunlight shining through two windows in one room.]
Now, the nature of the Shechinah is that she has nothing of her own. (לית לה מגרמא כלום) And what we refer to as Godliness (that which is hidden) is the source of all the Shechinah's emanations.
Normally, the ideal state of existence is the unification of the Shechinah with the Holy One Blessed be He. Now we aren't talking about two separate entities no matter how it may sound, we are simply talking about uniting the Revelation of Godliness, with the Hidden Godliness; it's all just God. (אין עוד מלבדו - there is none other than He) What this means in more practical or dynamic terms is that the revelation of Godliness is not missing from the world. Whenever a lack of Godliness becomes apparent, the Shechinah (its revelation) is said to be in exile. Because any need or emptiness is a function of the attribute of the Shechinah, of having nothing of her own.
So, now that we kind of understand that idea. We understand perhaps the smallest part of what it means to say the Shechinah is in exile. (If we were delving into this discussion with the aid of describing and explaining the sefirot, some of the points might be more accessible, but others might be more confusing, so we will leave the matter of sefirot aside from this post. For those who would like to see a little bit of the connection, suffice it to say that Malchut which is also called the Shechinah is the vessel within which all of creation (revelation of Godliness) occurs.)
Now, having some basic framework from which to work with, lets try and take another step: When we sin, we cause the Godliness that was invested in that sin to become deeply hidden. We cause less revellation of Godliness in the world, we cause the exile of the Shechinah. The Shechinah, now in exile, is pained or suffers because her poverty, her lack of anything of her own, is revealed to everyone through this apparent lack of Godliness.
When we pray for the sake of the completion of the Shechinah, for the union of the Shechinah with The Holy One Blessed Be He, it is the same as saying we are praying for Godliness to be openly revealed in the whole world. In this way, the Shechinah no longer lacks for anything, she is no longer in exile, she no longer suffers the embarrassment of 'abject poverty.'
When we pray in this way, it not only addresses all of our own needs and lacks but those of all the world, for every need in the world is merely an expression of the Shechinah's having nothing of her own.