Lekhah Dodi sung to welcome the Sabbath, has mystical origins.

Lekhah Dodi ('Come my friend') is the hymn sung during the synagogue service on Friday night to welcome the Sabbath. The opening stanza reads: 'Come my friend, to meet the bride; let us welcome the presence of the Sabbath'; and the other stanzas are in praise of the Sabbath and expressions of hope for the restoration of Zion and the Messianic redemption.

The practice of welcoming the Sabbath as Israel's bride is mentioned in the Talmud, and on the basis of this the sixteenth-century Kabbalists in Safed developed an elaborate ritual in which they would go out into the fields dressed in white garments to welcome the Sabbath, identified by them with the Shekhinah.
Solomon Alkabetz, the author of the Lekhah Dodi, was a member of this mystic brotherhood and composed the hymn especially for the ritual. The consecutive stanzas begin with the letters of his name to form the nominal acrostic, Shelomo Ha-Levi, 'Solomon the Levite'.
Lekhah Dodi is now recited in all Jewish congregations and various melodies have been composed with which to accompany it. The final stanza reads: 'Come in peace, thou crown of thy husband, with rejoicing and with cheerfulness, in the midst of the faithful of the chosen people; come, O bride, come, O bride.'
Very few modern writers appreciate that, for the Kabbalists, the 'husband' for whom the Sabbath is the crown is, following the doctrine of the Sefirot, the Sefirah Tiferet, the spouse of the Shekhinah.
The hymn is now sung, however, with no awareness of the original Kabbalistic nuances. It is the universal custom to turn towards the door when this stanza is sung and bow to welcome the Sabbath.

Rabbi Dr. Louis Jacobs (1920-2006) was a Masorti rabbi, the first leader of Masorti Judaism (also known as Conservative Judaism) in the United Kingdom, and a leading writer and thinker on Judaism.
M.S, adds:
 couple of adjustments to the explanation.
1.    lecha dodi should translate as "go my friend" and not "come my friend"
dodi could also be "my beloved".  myriad mistranslation abound on this phrase - lecha dodi.
2.    the mystical guy who started going out into the field to welcome shabbat was the Ari and Solomon Alkabetz was one of his contemporaries.
maybe it was Alkabetz who started the going out into the field.  he was the older one.  but who knows....buried in the sands of time.