13:46 Paul and Barnabas spoke out boldly, and said,
"It was necessary that God's word should be spoken to you first. 
Since indeed you thrust it from you,
and judge yourselves unworthy of eternal life, behold, we turn to the Gentiles. 

13:47 For so has the Lord commanded us, saying, 
'I have set you as a light for the Gentiles, 
That you should bring salvation to the uttermost parts of the earth.'"  (Is 42:6; 49:6)

13:49 The Lord's word was spread abroad throughout all the region. 
13:50 But the Jews stirred up the devout and prominent women and the chief men of the city,
and stirred up a persecution against Paul and Barnabas, and threw them out of their borders. 
13:51 But they shook off the dust of their feet against them, and came to Iconium. 
13:52 The disciples were filled with joy with the Holy Spirit. 
 

vs 45 The gospel was particularly humiliating to the religous elite Jewish mindset. It spoke of concepts of God which were reckoned heretical to Jew who rejected Jesus as the Messiah. Such hostility had been demonstrated by them throughout Jesus' ministry and that of the early church. Although they despised Gentiles, yet they wanted to be looked up to as the people of God among the Gentiles.  They wanted to be thought of as religiously superior. Such an attitude explains to a degree the contention among modern day Christians as well where one gets the impression that every church seems to thinks they're superior to every other church. 

As with many religously zealous people today, the Jews just didn't really listen to Paul nor to what the scriptures were saying. Such people tend to put human dogma above a proper interpretation of the text. Debating with such people simply becomes a shouting match as their presumptions prevent them from reasoning. Incapable of carrying on a rational conversation and unable to win the argument as they can't present a convincing argument sticking to the facts, they simply try to kill or vilify their opponents. Islam, Judaism, Christianity, and many political movements have all been guilty of this from time to time.

vs 46  There are those who claim that this was a dispensational shift in the direction of the gospel, as if Paul were speaking categorically. But in fact we see later on that from city to city he continues to visit synagogues and preaches to Jews. Here he is just referring to the particular case of this city. The necessity of preaching to Jews first was in accordance with God's design. He brought Christ into the world as a Jews who preached among Jews. The spread of the gospel starts from Jerusalem. So also it appears Paul applied this priniciple to individual cities, preaching first to Jews, then God fearing Gentiles and then to the society at large, which is a sort of demographic application. Some view this concept temporally as well, in which there was a time when the gospel was primarily spread to Jews, but now we are in the times of the Gentiles. 

What does Paul mean by "judge yourselves unworthy of everlasting life"? He is not saying that God judged them unworthy. He is saying that they judged themselves unworthy (contrary to some Christian's concept of election). Yet they would have claimed not to have done anything of the kind. What he implies is that people have to have a sense that they are qualified to received eternal life in accordance with God's way of doing things as is revealed in the gospel Paul preached. The qualification in the gospel is essentially faith in God's grace for the forgivness of sins provided by the atoning work of Christ on the cross. The Jews rejecting this concept willfully put themselves in the category of the unqualified.

vs 47 It is interesting that Paul is quoting a verse in the scriptures which was written concerning the Messiah, but applies it to himself. The apostle John writes, "in this world we are like him." 1John 4:17 And Paul says of himself "We are therefore Christ's ambassadors, as though God were making his appeal through us." 2Cor 5:20 See also The Following Jesus Series. Paul realized that God's intention was to extend the gospel to the world.

vs 48 I would imagine that many Gentiles had been attracted to the God of Israel but were not interested in becoming Jews and following all those Jewish customs. Now Paul comes with a message that you don't have to become a Jew to become a Christian, God accepts Gentiles as Gentiles if they simply put their faith in Christ, and it was well received.

"as many as were ordained to eternal life believed" has in interesting grammatical structure in the greek known as a pluperfect periphrastic. More precisely this is "as many as had been appointed to eternal life believed". "Appointed" is also more accurate than "ordained". The pluperfect indicates that their being appointed to eternal life was a once and for all accomplished event, which occurred before they believed. However Peter speaks of being "Elect according to the foreknowledge of God" 1Peter 1:2 which may be referring to being appointed to eternal life in accordance with God's foreknowledge of how we would respond to the gospel. Though contrary to Calvinism, such an interpretation preserves both the Biblical principles of the free will of man and the sovereignty of God. (And who is going to tell God He can't do it that way?) 

vs 49 Evangelism is one of the inevitable effects of true belief. 2Co 4:13  It is written: "I believed; therefore I have spoken." With that same spirit of faith we also believe and therefore speak.  And Paul speaking to the Thessalonian Christians says,"For we know, brothers loved by God, that he has chosen you because ... The Lord's message rang out from you not only in Macedonia and Achaia-- your faith in God has become known everywhere." 1Thess 1:4,8 True faith is hard to hide.

vs 50 It is apparent that the Greek society was more egalitarian, and perhaps even feminist, compared to the Jews. For he we see women in the society having clout. Not that they held political office but as in the case of Pilate's wife that they influenced their husbands to expel Paul. "As for my people, children are their oppressors, and women rule over them" Is 3:12 And also to be noted that this does appear to be a political action as opposed to being expelled by a lawless mob. But it is interesting that these women described as devout and honorable rejected the gospel, even acting with hostility against it. Religious eliteness was not limited to the Jews alone. Then and now the greatest hostility against the gospel comes from  those who reckon themselves the religious elite.

vs 51 Jesus taught "If people do not welcome you, shake the dust off your feet when you leave their town, as a testimony against them."Luke 9:5  Doing such say, "I don't want to have anything to do with you. I won't even take your dust with me." This of course was meant not for the whole town, but for those who rejected him. But what is the application today? If we are to walk as Jesus did, and as the apostles did, it seems appropriate to respond to such a degree of hostility against our message with a sort of rebuke, or whatever may be the modern equivalent of shaking the dust off our feet. 

vs 52 Suddenly these who came to believe are called "disciples", a word which refers to a learner or pupil. After coming to faith in Christ, one should reckon oneself a student of the faith. There's a lot more to be learned than just what comes from initially hearing the gospel. Another thing we notice here is joy in the face of hostility, which again indicates the quality of their faith. To pray a prayer with someone to receive Christ only to see no effects is not the kind of conversion characteristic of Biblical faith. Humility, confidence in the face of hostility,  endurance, hope, and love for the Christian community, these are characteristic of the response of Biblical faith.