Paul thanks God because God has enabled him to be faithful to the service to which he was appointed (v. 12). To “strengthen” someone is to give them the power of ability to do a particular task. This is the same verb (ἐνδυναμόω) Paul uses in Phil 4:13, and will use in 2 Tim 4:17. In both cases, Paul describes his weakness and inability to do the task God has given him, yet God gave him the strength to not only fulfill his commission, but to do so successfully.
Paul refers here to his commission to be a servant of God. The Greek noun διακονία can refer to any sort of job, assignment, or obligation. While we tend to think of “service” as those voluntary jobs we do for our church or school, the word can mean much more than that. In English we refer to someone who has been appointed to the role of an ambassador as being in the “foreign service.”
Paul also recalls his former life before his encounter with Jesus on the road to Damascus (v. 13, 16). He says that he was a “blasphemer, persecutor, and insolent opponent.” In English, the word blasphemy has taken on the connotation of speaking against a particular religious view. In the context of the book of Acts, Paul did not “blaspheme” by speaking slanderously about God, rather, he unintentionally blasphemed by speaking slanderously about Jesus, denying he was the messiah and denying that God raised him from the dead.
But in Greek, the words translated as blasphemy (βλάσφημος, βλασφημία, and the verb βλασφημέω) are usually associate with slander, demeaning speech, or even disrespectful talk. This might be mocking a particular view, a sarcastic parody, etc., usually with the intention of shaming people who believe that sort of thing. In a public debate, it is easier to mock the opponent rather than engage their ideas. This might be personal attacks, or using a straw-man argument. It is far easier to create a simplistic characterization of a person’s ideas and attack that rather than seriously examining what they actually say!
This fits well with the third word in this line, Paul was insolent. The noun (ὑβριστής) is rare in the New Testament, only appearing here and Rom 1:30 (a vice list). The word is also rare in the LXX (10 times), but it does appear in Prov 6:17 as one of the seven things the Lord hates (“haughty eyes”). The word appears in secular descriptions of vice in secular Greek as well. Aristotle describes the wealthy as “insolent and arrogant” (Rhet. 1390b, 33); “insolence means to do and say things that bring shame to the victim” (Rhet. 2, 2, via BDAG).
Taken with the slander implied with the Greek idea of blasphemy, perhaps we can think of this sort of speech as the lowest form political discourse, the old-fashioned “mudslinging” and yellow-press tactics which most politicians say they will not use (unlike their communist, atheist, baby killing, rap music loving opponent).
Since Paul was the “worst of sinners,” God’s demonstration of patience and mercy to him was a demonstration of how great God’s mercy can be. If God was merciful to Paul, of all people, then how much more will he be merciful to you? This is perhaps an intentional contrast with the false teachers he will mention in verse 20.
Paul therefore claims to have been called to serve God, but sees that calling as an example of God’s grace. Anyone who is called to any form of ministry ought to see their calling as just that, God lavishing his grace on someone who is unworthy. This humble way of thinking seems to me to be missing in too many western (American) ministries.