The Shechinah (שכינה) is not a separate entity from God. It is the point where God's hidden infinity first becomes visible, the way sunlight becomes visible only after it leaves the body of the sun. Rabbi Schneur Zalman of Liadi calls it the "world of manifestation," the "matron," the "mother of children," and Knesset Yisrael (כנסת ישראל), the collective source of all Jewish souls.
From this source, every individual creature receives precisely the light and vitality suited to it. But the source itself, the Shechinah in its full intensity, no world can endure directly. Even the highest angels would be annihilated by unfiltered contact with it, dissolved back into nothingness the way the sun's own light disappears within the body of the sun.
So the Shechinah needs a "garment," something that can contain its light without being annihilated by it. And that garment is the Torah. God's will and wisdom, clothed in the laws and narratives of Torah, can hold the infinite light in a form that worlds can receive. The Torah is both transparent to God's light and substantial enough to channel it downward.
In the First Temple, this garment was the Ten Commandments engraved on the Tablets in the Holy of Holies. The Shechinah dwelled there with a power and directness unmatched anywhere else, because the Ten Commandments are the all-encompassing principles of the entire Torah, drawn from Chochmah Ila'ah (חכמה עילאה), the supernal wisdom far above the ordinary chain of worlds.
After the Temple was destroyed, the Talmud teaches, God has only "the four cubits of halacha (Jewish religious law)h" (Berachot 8a). Every person who sits alone studying Torah becomes a Holy of Holies. The Shechinah rests with them. The garment has changed. The light has not.