​Hebrews 12:14

  • Follow peace with all [men], and holiness, without which no man shall see the Lord: (Hebrews 12:14)

There's a very similar verse found in Matthew that I'll include in here:
  • Blessed [are] the pure in heart: for they shall see God. (Matthew 5:8)

This is another in a series of verses that can be misunderstood and used to teach sinless perfectionism--the teaching that you need to be without sin to be saved--or Lordship Salvation, which adds works to the gospel in one way or another, before or after salvation.  That's because it can be taken to mean we have to, through effort, become holy enough to see the Lord.  This is a nicer way of saying you need to keep the law to be saved, which is a lie.

A contextual interpretation
The context of Hebrews 12 is all about living the Christian life and the consequences of Christians not doing so:
  • ¶ Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset [us], and let us run with patience the race that is set before us, (Hebrews 12:1)
  • ¶ Ye have not yet resisted unto blood, striving against sin. And ye have forgotten the exhortation which speaketh unto you as unto children, My son, despise not thou the chastening of the Lord, nor faint when thou art rebuked of him: For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth. (Hebrews 12:4-6) 
  • Furthermore we have had fathers of our flesh which corrected [us], and we gave [them] reverence: shall we not much rather be in subjection unto the Father of spirits, and live? For they verily for a few days chastened [us] after their own pleasure; but he for [our] profit, that [we] might be partakers of his holiness. (Hebrews 12:9-10)
With this in mind, verse 14 can be seen as an instruction to try to live the best Christian life we can, because other people won't see Christ in us if we don't, and may not believe the gospel.  We can do that, in part, by actingly peacably with them, and by not becoming bitter with them:
  • Looking diligently lest any man fail of the grace of God; lest any root of bitterness springing up trouble [you], and thereby many be defiled; (Hebrews 12:15) 

Another interpretation
It's very similar to verses I've tried to address like Colossians 1:23, these collections of verses, and the teaching about the difference between our flesh and our spirit (especially this one), because it's one of those verses that can be thought of as talking about our flesh instead of our spirit, and seeing the Lord can be equated with getting or being saved.  Please refer to those links at the start of the paragraph to see the clear scriptures that reveal the difference between our flesh and spirit, and how our spirit is perfect after we're saved but our flesh is not.

The unsaved, or unholy, can't yet see God, because of their sin and unbelief:
  • But your iniquities have separated between you and your God, and your sins have hid [his] face from you, that he will not hear. (Isaiah 59:2)
  • And the Father himself, which hath sent me, hath borne witness of me. Ye have neither heard his voice at any time, nor seen his shape. And ye have not his word abiding in you: for whom he hath sent, him ye believe not. (John 5:37-38)

In this instance, saints' perfected spirits (from those saints who die before the rapture) may see the Lord at some point, e.g.:
  • We are confident, [I say], and willing rather to be absent from the body, and to be present with the Lord. (2 Corinthians 5:8)
But I think their flesh will die before that.  I think it's possible this could also be interpreted as referring to those saints who have endured the tribulation period enough to make it to the rapture at the end, or even both meanings may apply.  If it's referring to saints who have died in the past as well as to those who made it to the end of the tribulation period, we'll all be given glorified (holy) bodies and will meet the Lord in the air, so it would make sense in that respect:
  • Who shall change our vile body, that it may be fashioned like unto his glorious body, according to the working whereby he is able even to subdue all things unto himself. (Philippians 3:21)
  • So also [is] the resurrection of the dead. It is sown in corruption; it is raised in incorruption: It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power: It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body. (1 Corinthians 15:42-44)
  • ¶ Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal [must] put on immortality. So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory. (1 Corinthians 15:51-54) 
  • Then we which are alive [and] remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. (1 Thessalonians 4:17)

To conclude, this is another verse that we need not take as an instruction to keep the law for our salvation.  And while I'm not sure about a lot of things in the Bible, this included, there are other understandable ways of appreciating this scripture beside one that corrupts the gospel.