To this end we always pray for you, that our God may make you worthy of His calling and may fulfill every resolve for good and every work of faith by His power, so that the name of our Lord Jesus may be glorified in you, and you in Him, according to the grace of our God and the Lord Jesus Christ. (2 Thess. 1:11-12, ESV)
The second prayer of 2 Thessalonians is related to the first prayer. Just to review, the first prayer was thanksgiving for sanctification. The second prayer is related: supplication for sanctification."
Paul and his companions (the we in verse 11) asked God to give power to the Thessalonians--power to be holy. By doing this, they modeled for all Christians the attitude of a godly Christian. Paul does not explicitly command the Thessalonians to pray this prayer, but I believe this prayer is a Christian duty. As Paul wrote in 1 Corinthians 11:1, "Be imitators of me, as I am of Christ." If we are to be imitators of Paul, for one thing, we should pray the same prayers that he prayed--including this one.
Why are to we pray for sanctification? Well, verse 12 says that this prayer glorifies God and those whom are sanctified by God's gracious giving of the Holy Spirit. This prayer honors the great Sanctifier, who gives power to be holy. It also, when the Lord answers this prayer, allows us to "become partakers of the divine nature, having escaped the corruption that is in the world because of sinful desire" (2 Peter 1:4). This is an important prayer! Let's not miss out on God's sanctifying power because of our laziness in prayer!
Let me conclude with an exhortation. (Note: I am not a pastor nor am I an expert in biblical exegesis, but I believe this is a correct application of what God is saying in these verses.)
Let us, as often as we can, pray for ourselves and our brothers: that the Lord would give us His power to be holy and worthy of His calling.