What Did jesus mean With "Every Branch Not Abiding In Me Will be Burned Up?"

I believe this particular passage is a warning to Israel concerning its impending destruction. It may be applied secondarily as a teaching concerning individual salvation - those that do not remain in Christ are not saved. A strong witness for the doctrine of preserverance.

 

Yes, a strong witness against eternal security or against perserverance of the saints. You have to abide in Him before you can stop abiding in Him.

 

Actually, a strong witness for Perserverance against OSAS. But as I said, that is a secondary application as far as I'm concerned. The primary meaning is the warning to Israel concerning the looming destruction due to their covenantal failure.

 

Romans 11:
17 If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, 18 do not consider yourself to be superior to those other branches. If you do, consider this: You do not support the root, but the root supports you. 19 You will say then, “Branches were broken off so that I could be grafted in.” 20 Granted. But they were broken off because of unbelief, and you stand by faith. Do not be arrogant, but tremble. 21 For if God did not spare the natural branches, he will not spare you either.
22 Consider therefore the kindness and sternness of God: sternness to those who fell, but kindness to you, provided that you continue in his kindness. Otherwise, you also will be cut off. 23 And if they do not persist in unbelief, they will be grafted in, for God is able to graft them in again.

1 John 2:
Warnings Against Denying the Son
18 Dear children, this is the last hour; and as you have heard that the antichrist is coming, even now many antichrists have come. This is how we know it is the last hour. 19 They went out from us, but they did not really belong to us. For if they had belonged to us, they would have remained with us; but their going showed that none of them belonged to us.
20 But you have an anointing from the Holy One, and all of you know the truth. 21 I do not write to you because you do not know the truth, but because you do know it and because no lie comes from the truth. 22 Who is the liar? It is whoever denies that Jesus is the Christ. Such a person is the antichrist—denying the Father and the Son. 23 No one who denies the Son has the Father; whoever acknowledges the Son has the Father also.
24 As for you, see that what you have heard from the beginning remains in you. If it does, you also will remain in the Son and in the Father. 25 And this is what he promised us—eternal life.
26 I am writing these things to you about those who are trying to lead you astray. 27 As for you, the anointing you received from him remains in you, and you do not need anyone to teach you. But as his anointing teaches you about all things and as that anointing is real, not counterfeit—just as it has taught you, remain in him.

Hebrews 3:
Warning Against Unbelief
7 So, as the Holy Spirit says:
“Today, if you hear his voice,
8 do not harden your hearts
as you did in the rebellion,
during the time of testing in the wilderness,
9 where your ancestors tested and tried me,
though for forty years they saw what I did.
10 That is why I was angry with that generation;
I said, ‘Their hearts are always going astray,
and they have not known my ways.’
11 So I declared on oath in my anger,
‘They shall never enter my rest.’ ”
12 See to it, brothers and sisters, that none of you has a sinful, unbelieving heart that turns away from the living God. 13 But encourage one another daily, as long as it is called “Today,” so that none of you may be hardened by sin’s deceitfulness. 14 We have come to share in Christ, if indeed we hold our original conviction firmly to the very end. 15 As has just been said:
“Today, if you hear his voice,
do not harden your hearts
as you did in the rebellion.”
16 Who were they who heard and rebelled? Were they not all those Moses led out of Egypt? 17 And with whom was he angry for forty years? Was it not with those who sinned, whose bodies perished in the wilderness? 18 And to whom did God swear that they would never enter his rest if not to those who disobeyed? 19 So we see that they were not able to enter, because of their unbelief.