Shekhinah (- alternative transliterations Shekinah, Shechinah, Shekina, Shechina, Schechinah, שכינה) is the English spelling of a feminine Hebrew language word that means the dwelling or settling, and is used to denote the dwelling or settling presence of God, especially in the Temple in Jerusalem.
Shechinah is derived from the Hebrew verb שכן. In Biblical Hebrew the word means literally to settle, inhabit, or dwell, and is used frequently in the Hebrew Bible. (See Exodus 40:35 - "Moses could not enter the Tent of Meeting, for the cloud rested [shakhan] upon it, and the glory of the Lord filled the Tabernacle." See also e.g. Genesis 9:27, 14:13, Psalms 37:3, Jeremiah 33:16), as well as the weekly Shabbat blessing recited in the Temple in Jerusalem ("May He who causes His name to dwell [shochan] in this House, cause to dwell among you love and brotherliness, peace and friendship"). In Mishnaic Hebrew the word is often used to refer to bird's nesting and nests. ("Every bird nests [shechinot] with its kind, and man with its like, Talmud Baba Kammah 92b.) and can also mean "neighbor" ("If a neighbor and a scholar, the scholar is preferred" Talmud Ketubot 85b). The word "Shechinah" also means "royalty" or "royal residence" (The Greek word σκήνη - dwelling - is thought to be derived from שכינה and שכן. ) The word for Tabernacle, mishcan, is a derivative of the same root and is also used in the sense of dwelling-place in the Bible, e.g. Psalm 132:5 ("Before I find a place for God, mishcanot (dwelling-places) for the Strong One of Israel.") Accordingly, in classic Jewish thought, the Shekhina refers to a dwelling or settling in a special sense, a dwelling or settling of divine presence, to the effect that, while in proximity to the Shekhinah, the connection to God is more readily perceivable.
According to Professor Kern, Shekinah means "the presence of God." 
The Shekhinah is referred to as manifest in the Tabernacle and the Temple in Jerusalem throughout Rabbinic literature. It is also reported as being present in the acts of public prayer, ("Whenever ten are gathered for prayer, there the Shechinah rests" Talmud Sanhedrin 39a); righteous judgment ("when three sit as judges, the Shechinah is with them." Talmud Berachot 6a), and personal need ("The Shechinah dwells over the headside of the sick man's bed" Talmud Shabbat 12b; "Wheresoever they were exiled, the Shechinah went with them." Megillah 29a).
The Talmud expounds a Beraita (oral tradition) which illuminates the manner in which the Kohen Gadol (High Priest) is to sprinkle the blood of the bull-offering towards the Parochet (Curtain) separating the Hekhal (sanctuary) from the Kadosh Kadoshim (Holy of Holies):
"[And so shall he do in the midst of the Tent of Meeting] that dwells (shokhen) among them in the midst of their impurities (Leviticus 16:16). Even at a time when the Jews are impure, the Shekhinah (Divine Presence) is with them.
A certain Sadducee said to Rabbi Chanina: Now [that you have been exiled, you are certainly impure, as it is written: "Her impurity is [visible] on her hems." (Lamentations 1:9). He [Rabbi Chanina] said to him: Come see what is written regarding them: [The Tent of Meeting] that dwells among them in the midst of their impurities. Even in a time that they are impure, the Divine Presence is among them. Talmud Tractate Yoma 56b
The Talmud reports that the Shekhinah is what caused prophets to prophesy and King David to compose his Psalms The Shechinah manifests itself as a form of joy, connected with prophecy and creativity: Talmud Pesachim 117a) The Talmud also reports that "The Shechinah does not rest amidst laziness, nor amidst laughter, nor amidst lightheadedness, nor amidst idle conversation. Rather, it is amidst the joy associated with a mitzvah that the Shechinah comes to rest upon people, as it is said: 'And now, bring me for a musician, and it happened that when the music played, God's hand rested upon him' [Elisha] [2 Kings 3:15]" (Pesachim 117a). Thus the Shekhinah is associated with the transformational "Spirit of God" regarded as the source of prophecy:
After that thou shalt come to the hill of God, where is the garrison of the Philistines; and it shall come to pass, when thou art come thither to the city, that thou shalt meet a band of prophets coming down from the high place with a psaltery, and a timbrel, and a pipe, and a harp, before them; and they will be prophesying.
And the spirit of the LORD will come mightily upon thee, and thou shalt prophesy with them, and shalt be turned into another man. (1 Samuel 10:5-6 JPS).
The prophets made numerous references to metaphorical visions of the presence of God, particularly in the context of the Tabernacle or Temple, particularly visions of thrones or robes that fill the Sanctuary, that are traditionally associated with and described as visions of the Shekhinah. Isaiah wrote "I saw the Lord sitting upon a throne high and lifted up, and his train filled the Temple." (Isaiah 6:1). Jeremiah implored "Do not dishonor the throne of your glory" (Jeremiah 14:21) and referred to "Thou throne of glory, on high from the beginning, Thou place of our sanctuary" (Jeremiah 17:12). Ezekiel spoke of "the glory of the God of Israel was there [in the Sanctuary], according to the vision that I saw in the plain."
"I sing in
to enter the gates
of the Field
of holy apples.
"A new table
we prepare for Her,
a lovely candelabrum
sheds its light upon us.
"Between right and
the Bride approaches,
in holy jewels
and festive garments..."
A paragraph in the Zohar starts: "One must prepare a comfortable seat with several cushions and embroidered covers, from all that is found in the house, like one who prepares a canopy for a bride. For the Shabbat is a queen and a bride. This is why the masters of the Mishna used to go out on the eve of Shabbat to receive her on the road, and used to say: 'Come, O bride, come, O bride!' And one must sing and rejoice at the table in her honor ... one must receive the Lady with many lighted candles, many enjoyments, beautiful clothes, and a house embellished with many fine appointments ..."
The tradition of the Shechinah as the Shabbat Bride, the Shabbat Hamalka, continues to this day.
In addition to the various accounts indicating the presence or glory of God recorded in the Hebrew Bible, many Christians also consider the Shekhinah to be manifest in numerous instances in the New Testament.
The public domain Easton's Bible Dictionary, published in 1897, says:
Shechinah – a Chaldee word meaning resting-place, not found in Scripture, but used by the later Jews to designate the visible symbol of God's presence in the Tabernacle, and afterwards in Solomon's temple. When the Lord led Israel out of Egypt, he went before them "in a pillar of a cloud." This was the symbol of his presence with his people. God also spoke to Moses through the 'shekhinah' out of a burning bush. For references made to it during the wilderness wanderings, see Exodus 14:20; 40:34-38; Leviticus 9:23, 24; Numbers 14:10; 16:19, 42.
It is probable that after the entrance into Canaan this glory-cloud settled in the tabernacle upon the ark of the covenant in the most holy place. We have, however, no special reference to it till the consecration of the temple by Solomon, when it filled the whole house with its glory, so that the priests could not stand to minister (1 Kings 8:10-13; 2 Chr. 5:13, 14; 7:1-3). Probably it remained in the first temple in the holy of holies as the symbol of Jehovah's presence so long as that temple stood. It afterwards disappeared. 
And Moses went up into the mount, and the cloud covered the mount. And the glory of Jehovah abode upon mount Sinai, and the cloud covered it six days: and the seventh day he called unto Moses out of the midst of the cloud. And the appearance of the glory of Jehovah was like devouring fire on the top of the mount in the eyes of the children of Israel. (Exodus 24:15-17 ASV)
The Shekhinah in the New Testament is commonly equated to the presence or indwelling of the Spirit of the Lord (generally referred to as the Holy Spirit, or Spirit of Christ) in the believer, drawing parallels to the presence of God in Solomon's Temple. Furthermore, in the same manner that the Shekhinah is linked to prophecy in Judaism, so it is in Christianity:
For no prophecy ever came by the will of man: but men spake from God, being moved by the Holy Spirit. (2 Peter 1:21 ASV)
Where references are made to the Shekhinah as manifestations of the glory of the Lord associated with his presence, Christians find numerous occurrences in the New Testament in both literal (as in Luke 2:9 which refers to the "glory of the Lord" shining on the shepherds at Jesus' birth) as well as spiritual forms (as in John 17:22, where Jesus speaks to God of giving the "glory" that God gave to him to the people). A contrast can be found in Ichabod, so named as a result of the Ark of the Covenant being captured by the Philistines - "The glory is departed from Israel" (1 Samuel 4:22 KJV).
By day the LORD went ahead of them in a pillar of cloud to guide them on their way and by night in a pillar of fire to give them light, so that they could travel by day or night, Exodus 13:21.
Picture of Shekinah (Melchizedek's semi-material presense)
tents around sacred place of worship the Tabernacle. Melchizedek's
presense(Shekinah) at night was like a fire and during the day it was a
cloud that moved and led the Israelites.
Picture of the inside of the entire Tabernacle. Melchizedek's presense was over the Holy of Holies. Only the High Priest could enter it once a year on The Day of Atonement.