In Titus 2:11-12, Paul closes up his exhortation about teaching to Titus begun in Titus 2:1 by giving the reason for the commands of verses 1-10.

Summary: There are two finite verbs in this passage connected by a purpose clause, so they sum up the main point of this passage:  The grace of God was revealed so that we might live holy lives. 

Translating and Arcing Commentary: I took the adjective soterios as a substantival adjective explaining (Ex) what the grace of God was (Id) – The grace of God is salvation for all people.  This links with the fact that Paul just wrote instructions for older men, older women, younger women, younger men, and slaves earlier in Titus 2.  This grace for salvation has come to all, old, young, male, female and slaves. 

The feminine present participle “training us” describes what the grace of God does when it appears.  Thus, it stands as a purpose (Pur) for this appearing (Ac).  Grace that brings salvation does not merely leave us with a deliverance from our guilt, but it actively is training us.

For what? Verse 12b introduces the purpose (Pur) for the training (Ac) with the phrase in order that.  Then Paul contrasts a former way of life that was renounced, ungodliness and worldly lusts (-), with the new way of life that we now live: soberly, upright, and holy (+). 

To sum it all up - We’re not left in our sins but freed from our guilt, and on top of that, God not only saves us but trains us for godly living through his grace. 

So we ought not to feel like we’re on our own in this battle against ungodliness, the grace that has saved us is actively training us to live in holiness.  What good news!