The exact same Greek words ("sound doctrine" in Titus 2:1) also occur in three other of Paul's writings -
1 Timothy 1:8-11 (NASB)
8 But we know that the Law is good, if one uses it lawfully, 9 realizing the fact that law is not made for a righteous person, but for those who are lawless and rebellious, for the ungodly and sinners, for the unholy and profane, for those who kill their fathers or mothers, for murderers 10 and immoral men and homosexuals and kidnappers and liars and perjurers, and whatever else is contrary to sound teaching, 11 according to the glorious gospel of the blessed God, with which I have been entrusted.
The Greek word for "sound" is ὑγιαίνω, and the Greek word for "teaching" is διδασκαλία, which is also translated as "doctrine," as the following two passages indicate.
2 Timothy 4:1-3 (NASB)
1 I solemnly charge you in the presence of God and of Christ Jesus, who is to judge the living and the dead, and by His appearing and His kingdom: 2 preach the word; be ready in season and out of season; reprove, rebuke, exhort, with great patience and instruction. 3 For the time will come when they will not endure sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires...
Finally, the same words occur earlier in the Epistle to Titus.
Titus 1:7-9 (NASB)
7 For the overseer must be above reproach as God’s steward, not self-willed, not quick-tempered, not addicted to wine, not pugnacious, not fond of sordid gain, 8 but hospitable, loving what is good, sensible, just, devout, self-controlled, 9 holding fast the faithful word which is in accordance with the teaching, so that he will be able both to exhort in sound doctrine and to refute those who contradict.
While there is not much variation of the word διδασκαλία, which means teaching or doctrine in the New Testament, the word ὑγιαίνω has one other major connotation in the New Testament. That is, the word means healthy (physically "sound") such as is found in Luke 5:31; Luke 7:10; Luke 15:27; and 3 John 1:2. Thus there is healthy ("sound") teaching or doctrine, and unhealthy ("unsound") teaching or doctrine.
In the following verses, the Apostle Paul defines the "line" where the good doctrine turns into bad doctrine. The first "rule" is that the teaching must "boast in the cross of our Lord Jesus Christ" as the following verses indicate.
Galatians 6:11-16 (NASB)
11 See with what large letters I am writing to you with my own hand. 12 Those who desire to make a good showing in the flesh try to compel you to be circumcised, simply so that they will not be persecuted for the cross of Christ. 13 For those who are circumcised do not even keep the Law themselves, but they desire to have you circumcised so that they may boast in your flesh. 14 But may it never be that I would boast, except in the cross of our Lord Jesus Christ, through which the world has been crucified to me, and I to the world. 15 For neither is circumcision anything, nor uncircumcision, but a new creation. 16 And those who will walk by this rule, peace and mercy be upon them, and upon the Israel of God.
The "rule" is the boasting in the cross of Christ. Sound teaching therefore must direct its "boasting" to the cross of Christ. (For example, the unsound teaching or legalism of circumcision in the Galatian church detracted from the boasting in the cross of Christ.) There is also one more "rule" mentioned by the Apostle Paul with regard to teaching.
1 Timothy 6:11-16 (NASB)
11 But flee from these things, you man of God, and pursue righteousness, godliness, faith, love, perseverance and gentleness. 12 Fight the good fight of faith; take hold of the eternal life to which you were called, and you made the good confession in the presence of many witnesses. 13 I charge you in the presence of God, who gives life to all things, and of Christ Jesus, who testified the good confession before Pontius Pilate, 14 that you keep the commandment without stain or reproach until the appearing of our Lord Jesus Christ, 15 which He will bring about at the proper time—He who is the blessed and only Sovereign, the King of kings and Lord of lords, 16 who alone possesses immortality and dwells in unapproachable light, whom no man has seen or can see. To Him be honor and eternal dominion! Amen.
This "commandment" is that we believe in the name of His Son Jesus Christ, and love one another, just as He commanded us (1 John 3:23). In other words, sound teaching can only come from those who know the Lord--that is, those who believe in the name of the Lord Jesus Christ. Secondly, the teaching must be edifying, or loving to those who hear.
The spiritual gift of the exposition of the Bible (teaching) is therefore meant for edification (1 Cor 14:26) through the "boasting" of the cross of Christ. That is the meaning of "sound doctrine."