The 'Presence' of the Lord
Genesis 3:8 8 ¶ And they heard the sound of the LORD God walking in the garden in the cool of the day, and Adam and his wife hid themselves from the presence of the LORD God among the trees of the garden.
To be in the "presence" of the Lord is to be seen by him.Genesis 4:16 16 Then Cain went out from the presence of the LORD and dwelt in the land of Nod on the east of Eden.
Cain certainly could not escape the Lord's omnipresence. So, there is a more local presence connected with this statement. Cain moved away from the center of that culture that remembered and called upon the Lord, and lived in his "presence."
Genesis 27:7 7 'Bring me game and make savory food for me, that I may eat it and bless you in the presence of the LORD before my death.'
The pronunciation of the blessing of the Lord implies the "presence" of the Lord.
Exodus 33:13-16 13 "Now therefore, I pray, if I have found grace in Your sight, show me now Your way, that I may know You and that I may find grace in Your sight. And consider that this nation is Your people." 14 And He said, "My Presence will go with you, and I will give you rest." 15 Then he said to Him, "If Your Presence does not go with us, do not bring us up from here. 16 "For how then will it be known that Your people and I have found grace in Your sight, except You go with us? So we shall be separate, Your people and I, from all the people who are upon the face of the earth."
So, the "Presence" is not just omni-presence. It is a special presence, without which the doing of life has no meaning.
Deuteronomy 4:37 37 "And because He loved your fathers, therefore He chose their descendants after them; and He brought you out of Egypt with His Presence, with His mighty power,
The "Presence" of the Lord brought out the Israelites. The special manifestation, from the Burning Bush to the Exodus was actuated and led by the Presence of the Lord.
2 Kings 24:20 20 ¶ For because of the anger of the LORD this happened in Jerusalem and Judah, that He finally cast them out from His presence. Then Zedekiah rebelled against the king of Babylon.
The casting out from the Lord's Presence meant the deportation to Babylon. This certainly did not mean that God ceased to care for them, because he still sent them prophets in Babylon (Ezekiel). But, remember that the Temple -- the only place at which the propitiatory sacrifices were ordained to be made -- had been torn down. By being ostracized from the temple, they were away from the Lord's Presence.
Our New Covenant worship needs the "presence" of the Lord in this special way, and has it as we please him by worshiping in spirit and truth, with circumcision of the heart.