We find the Biblical meaning of establish in what God our Father and our Lord Jesus Christ has done and is doing for us.
In the Scripture preceding his blessing found in 2 Thessalonians 2:16-17, Paul sums up how we are established. God loved us, chose us for salvation (1 Th 1:4; 2 Th 5:23-24; Ro 9:11; 11:5; Eph 1:4) through sanctification of the Spirit (1 Th 4:3-4; Ro 6:19; 1 Co 1:30; 1 Tm 2:15; Heb 12:14; 1 Pt 1:2) and belief in the truth (Eph 2:4-10; John 14:6; 18:37) and called us through the gospel of the kingdom (1 Th 1:5; Ro 2:16; 10:14) “for the obtaining of the glory of our Lord Yeshua the Messiah” (2 Th 2:14; Col 1:27; Ro 5:2; Eph 1:18) in the new heaven and new earth (Rev 21:1-4).
Here’s how Paul was inspired to put it:
13 But we are bound to always give thanks to God for you, brothers [and sisters] loved by the Lord, because God chose you from the beginning for salvation through sanctification of the Spirit and belief in the truth, 14 to which he called you through our Good News, for the obtaining of the glory of our Lord Yeshua the Messiah.
15 So then, brothers, stand firm and hold the traditions which you were taught by us, whether by word or by letter. 2 Thessalonians 2:13-15
There, we see the primary ways God establishes us as His people fit for the kingdom.
Paul wrote the forgoing in context with trials and tribulations we face.
1 Now, brothers [and sisters], concerning the coming of our Lord Yeshua the Messiah and our gathering together to him, we ask you 2 not to be quickly shaken in your mind, and not be troubled, either by spirit, or by word, or by letter as if from us, saying that the day of Messiah has already come. 3 Let no one deceive you in any way. For it will not be, unless the rebellion* comes first, and the man of sin is revealed, the son of destruction, 4 he who opposes and exalts himself against all that is called God or that is worshiped, so that he sits as God in the temple of God, setting himself up as God. 5 Don’t you remember that, when I was still with you, I told you these things? 6 Now you know what is restraining him, to the end that he may be revealed in his own season. 7 For the mystery of lawlessness already works. Only there is one who restrains now, until he is taken out of the way. 8 Then the lawless one will be revealed, whom the Lord will kill with the breath of his mouth, and destroy by the manifestation of his coming; 9 even he whose coming is according to the working of Satan with all power and signs and lying wonders, 10 and with all deception of wickedness for those who are being lost, because they didn’t receive the love of the truth, that they might be saved. 11 Because of this, God sends them a working of error, that they should believe a lie; 12 that they all might be judged who didn’t believe the truth, but had pleasure in unrighteousness. 2 Thessalonians 2:1-12
In the description of the most formidable troubles eternal election is often introduced as the shelter of the saints (Mt 24:22-31; 17:8). But that which comes first is not the triumphal song of Ro 8, but the way of righteousness (Ro 1–7). Election [“God chose you from the beginning for salvation”] provides a secret deposit; sanctification is election disclosed; and the root of that is faith in the truth. RIEGER
Now, we come to application of what God has made us. Paul writes this blessing to the Thessalonians and to us:
16 Now our Lord Yeshua the Messiah himself, and God our Father, who loved us and gave us eternal comfort and good hope through grace, 17 comfort your hearts and establish you in every good work and word. 2 Thessalonians 2:16-17