It is impossible to do justice to this small word in any length of time or print. Aside from the fact that it has a multiplicity of meanings from its Hebrew root, its usage across centuries of Jewish experience makes "sh'khina" impossible to capture in words. (The suffix "to" is the possessive "his.")
At its very basic meaning, the root of sh'khina might best be translated as "dwell." Even in English the word implies a variety of activities. It means more than live or reside. It carries with it a sense of deep personal investment (think of what it means to "dwell on the matter.") It means to make some place home, a place you can feel welcome dependably and be dependably located by others. All of these ideas are part of the word sh'khina.
Yet, because it has been employed across the many periods of Jewish history as a reference to God, it is rare to find this particular word used to refer to anything other than God. Translating it as "presence" is accurate because of the economy of words, but imprecise. Adding the adjectives "in-dwelling" or "abiding" adds some accuracy but adds a pretentious tone that impairs the implied intimacy. Equating it somehow with God's spirit makes sh'khina sound like something separate from the wholeness of God, or some incarnation of God that limits the ubiquitousness of the Holy One.
(It also sounds a little Christian to our ears. English-speakers often pronounce the word "she-KYE-na," to rhyme with "Red China," and imagine it to be the equivalent of the Holy Spirit in the Christian trinity.)
If I had to choose a single word for sh'khina (which I don't!), I would likely choose "pervasiveness." Sh'khina is the palpable presence of God in every facet of our existence – space, time, thought, relationship, even the thrumming of our bodies. Mysterious and transcendant though God may be, the integration of God into the world of God's creation is perceived by us as something indescribable that is nonetheless intimately familiar, the way a new acquaintance sometimes feels like an old friend or the realization of true love feels both unknown and recognizable at the same time.
Is sh'khina cause or effect – a manifestation of God or our attempt to name the phenomenon of encountering the Divine? Is it a name God has chosen or one we invented? Others can argue about it. It appears in our literature to overcome the distance between God's distant majesty and our yearning for something about God that touches our hearts.