"And he built there an altar, and named that place, To God, who made His Shekhinah to dwell in Bethel, because there had been revealed to him the angels of the Lord, in his flight from before Esau his brother." Targum Pseudo-Jonathan (Genesis 35:7) expands the plain text's brief naming into a full theological statement.
The plain Hebrew calls the place El Beit-El — the God of the House of God. The Targum renders the name through the vocabulary of Jewish mysticism: Shekhinah, the indwelling Presence, and the revelation of angels. These are the terms that would later become the foundation of Kabbalah.
What is the Shekhinah?
The Shekhinah is the dimension of God that dwells. It is God insofar as He takes up residence among His people — in the Tabernacle, in the Temple, in the hearts of the righteous. When Targum Pseudo-Jonathan says God "made His Shekhinah to dwell in Bethel," it is using the language of the later sanctuaries, projecting the Temple theology of its own era back onto Jacob's altar.
And this is the point. Bethel was not a one-time vision. It became a permanent place of divine dwelling. The stone Jacob laid his head on was the foundation stone of a theology that would eventually include the Mishkan, the Temple in Jerusalem, and every synagogue wherever Jews gather.
The takeaway: every place where you truly meet God becomes a House of God — and God stays, long after you have gone.