The meaning of "apart" in the Bible is pretty straightforward; it means there is a separation in spiritual states. What those states are and how the separation comes to be is a matter of context.

(Odkazy: Arcana Coelestia 4025, 7443, 9409)

9409. 'And on the children of Israel who had been set apart' means those restricted to the outward sense, separated from the inward. This is clear from the representation of 'the children of Israel who had been set apart' - that is, those who had been separated from Moses, Aaron, Nadab and Abihu, and the seventy elders, and about whom verse 2 above says 'they shall not come up' - as those restricted to the outward sense of the Word, separated from the inward, dealt with above in 9380. Something brief must be stated here about who exactly those people are, and what they are like, who are restricted to the outward sense of the Word, separated from the inward. They are those who draw no teachings about charity and faith from the Word but confine themselves to the sense of the letter. Teachings about charity and faith compose the inward substance of the Word, while the sense of the letter composes its outward form. The worship too of those restricted to the outward sense of the Word without the inward is something outward devoid of anything inward. They venerate outward things as being holy and Divine, and also believe that these things are in themselves holy and Divine, when in fact they are holy and Divine by virtue of inner realities. This was what the children of Jacob were like, see 3479, 4281, 4293, 4307, 4429, 4433, 4680, 4844, 4847, 4865, 4868, 4874, 4899, 4903, 4911, 4913, 6304, 8588, 8788, 8806, 8871.

[2] But let some examples serve to illustrate this matter. They believed that they were pure, free from all sin and all guilt, when they offered sacrifices and ate from them. For they thought that the sacrifices in their outward form alone, without the inward, were the most holy things of worship, that when used in those sacrifices the oxen, young bulls, lambs, she-goats, sheep, rams, and he-goats were holy, and that the altar was the most holy thing of all. And they thought of the bread of the minchahs and the wine of the drink-offerings in a similar way. They also believed that when they had washed their clothes and their bodies they were altogether clean, and in like manner that the perpetual fire on the altar and the fires in the lamps were in themselves holy, also the loaves of the presence, the anointing oil, and all else. This was what they believed because they rejected everything internal, so completely that they were unwilling even to hear about internal things, such as that they should love Jehovah for His sake and not their own, that is to say, not in order that they might be raised to important positions and wealth above all nations and peoples throughout the world. Nor therefore were they willing to hear that the Messiah was going to come for the sake of their eternal salvation and happiness, only for the sake of their pre-eminence over all in the world. Nor were they willing to hear about mutual love and charity towards the neighbour for the neighbour's sake and good, only for their own, so far as the neighbour was favourably disposed towards them. They thought nothing of entertaining feelings of enmity, harbouring hatred, taking vengeance, acting savagely, so long as they could lay hold of some reason.

[3] Their beliefs and actions would have been altogether different if they had been willing to accept teachings about love to and faith in the Lord and charity towards the neighbour. They would then have known and believed that burnt offerings, sacrifices, minchahs, drink-offerings, and feasting on sacrifices would not purify them from any guilt or sin, but that worship of God and heartfelt repentance would do so, Deuteronomy 33:19; Jeremiah 7:21-23; Micah 6:6-8; Hosea 6:6; Psalms 40:6, 8; 51:16-17; 1 Samuel 15:22. They would in a similar way have known that the washing of clothes and body rendered no one clean, only purification of the heart; and in like manner that the fire on the altar and fires in the lamps, also the loaves of the presence, and the anointing oil were not holy of themselves but by virtue of the inner realities which they were the signs of. They would have known too that when they were governed by those holy and inner realities they would be holy people, not on their own account, but on that of the Lord from whom everything holy springs. The children of Israel would have known these inner realities if they had received teachings about love and charity, because these declare what it is that outward things include within them. Those teachings also provide knowledge of the internal sense of the Word, because the internal sense of the Word constitutes true teachings about love to the Lord and charity towards the neighbour. It is also what the Lord teaches, when He says that on both these commands all the Law and the Prophets depend, Matthew 22:36, 40.

[4] The situation is virtually the same today in the Christian world. Here people are restricted to outward things, without anything inward, because teachings about love to the Lord and charity towards the neighbour are lacking, so much so that there is scarcely any knowledge of what celestial love is and what spiritual love is, which is charity. For the good of celestial and spiritual love, and consequently the truth of faith, constitute the inner level in a person. So it is that even at the present day the outward sense of the Word, without doctrinal teachings as regulator and guide, can be distorted as much as anyone likes. For teachings about faith without teachings about love and charity are like the darkness of night, whereas teachings about faith arising out of teachings about love and charity are like the light of day. For the good that belongs to love and charity is like the flame, while the truth of faith is like the light radiating from it.

[5] This being what people in the Christian world are like at the present day, that is to say, people restricted to outward things without anything inward, scarcely any have an affection for truth for its own sake. Here also is the reason why they are not even aware of what good, charity, or the neighbour is. They are not even aware of what the inner level in a person is, nor of what heaven is and hell is, nor of the fact that everyone is alive immediately after death. And those among them who keep to the teachings of their Church do not care whether those teachings are false or true. They learn them and endorse them not for the sake of exercising the good of charity from the heart, nor for the sake of the salvation of their soul and eternal happiness, but for the sake of getting on in the world, that is, to earn reputation, important positions, and wealth. For this reason they receive no enlightenment when they read the Word, and so will altogether deny the existence of anything inwardly present in the Word apart from what stands out in the letter. But more on this subject from experience will in the Lord's Divine mercy be stated elsewhere.