The first paragraph of Shema, one of Judaism's two central prayers, consists of verses from Deuteronomy chapter 6. Except that after the first line, Shema Yisrael, another line is interpolated, "Baruch shem k'vod" that does not appear in the Bible.
According to the Talmud, Jacob feared that his children might have strayed, spiritually (Pesachim 56a). To allay his fears, his sons recited in unison Shema Yisrael.
Jacob's response, the Talmud tells us was "Baruch shem k'vod malchuto l'olam va'ed", ("Blessed is the name of God's glorious kingdom for ever and ever"). Full of gratitude to God for children who all followed in his path, Jacob exclaimed this praise of God.
In Temple times, during the Yom Kippur service, the High Priest would recite the God's ineffable name. The people would respond, Baruch shem k'vod.
This verse, it seems, is a prayer for the continuation of the spiritual elevation that is part of Shema and the Yom Kippur service.