Havdalah is Hebrew for separation. It refers to separating the sacred from the ordinary, the sacred being the Sabbath day and the ordinary being the other days of the week.
The Havdalah service formally ends the Sabbath day and ushers in the regular week when we are once again engaged in our worldly concerns. We live in a world of opposites.
At the end of the Sabbath we are acutely aware of the tensions between these worlds, being the spiritual and the carnal worlds.
James 1: Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world.
2Cor.6 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
 And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?
 And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.
 Wherefore come out from among them, and be ye separate, saith the Lord, and touch not the unclean thing; and I will receive you, And will be a Father unto you, and ye shall be my sons and daughters, saith the Lord Almighty.
1Cor.10 But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils.
Eph.5 And have no fellowship with the unfruitful works of darkness, but rather reprove them
 For it is a shame even to speak of those things which are done of them in secret.
Exod.33 For wherein shall it be known here that I and thy people have found grace in thy sight? is it not in that thou goest with us? so shall we be separated, I and thy people, from all the people that are upon the face of the earth.
Lev.20 But I have said unto you, Ye shall inherit their land, and I will give it unto you to possess it, a land that floweth with milk and honey: I am the LORD your God, which have separated you from other people.  Ye shall therefore put difference between clean beasts and unclean, and between unclean fowls and clean: and ye shall not make your souls abominable by beast, or by fowl, or by any manner of living thing that creepeth on the ground, which I have separated from you as unclean.
Neh.9 And the seed of Israel separated themselves from all strangers, and stood and confessed their sins, and the iniquities of their fathers.
Neh.13 Now it came to pass, when they had heard the law, that they separated from Israel all the mixed multitude.
Prov.18 Through desire a man, having separated himself, seeketh and intermeddleth with all wisdom.
Matt.25 And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats: And he shall set the sheep on his right hand, but the goats on the left.
Rom.1 Paul, a servant of Jesus Christ, called to be an apostle, separated unto the gospel of God,
 My son, if sinners entice thee, consent thou not.
21 And the children of Israel, which were come again out of captivity, and all such as had separated themselves unto them from the filthiness of the heathen of the land, to seek the LORD God of Israel, did eat,
22 And kept the feast of unleavened bread seven days with joy: for the LORD had made them joyful, and turned the heart of the king of Assyria unto them, to strengthen their hands in the work of the house of God, the God of Israel.
¶ Then I proclaimed a fast there, at the river of Ahava, that we might afflict ourselves before our God, to seek of him a right way for us, and for our little ones, and for all our substance.
22 For I was ashamed to require of the king a band of soldiers and horsemen to help us against the enemy in the way: because we had spoken unto the king, saying, The hand of our God [is] upon all them for good that seek him; but his power and his wrath [is] against all them that forsake him.
23 So we fasted and besought our God for this: and he was intreated of us.
And Ezra the priest stood up, and said unto them, Ye have transgressed, and have taken strange wives, to increase the trespass of Israel.
11 Now therefore make confession unto the LORD God of your fathers, and do his pleasure: and separate yourselves from the people of the land, and from the strange wives.
Col.2: For I would that ye knew what great conflict I have for you, and for them at Laodicea, and for as many as have not seen my face in the flesh;
 Wherefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances,