The last words of the book of Acts in the Greek are “boldly and without hindrance.” This is a good theme to leave the book of Acts, that Paul preached the gospel boldly and without hindrance.
To speak “boldly” (παρρησία) is to have freedom to speak, perhaps even fearless speech. “Boldness” is a characteristic of apostolic preaching in the first part of Acts. The Sanhedrin saw that Peter and John spoke boldly (4:13), and the Jerusalem church prayed that God would continue to give them boldness (4:29); when they were filled with the Holy Spirit they did in fact speak with boldness (4:31).
But the word also has the nuance of confidence, knowing that you are speaking the truth; that you know the right answer, etc. In Acts 2:29 Peter makes an argument based on Scripture that Jesus is the Messiah, he says this “with confidence.” This is the confidence which I began with – knowing that something is certainly true gives you a confidence and boldness which a “guess” does not. Paul can speak from his house arrest with confidence because he knows the gospel he proclaims is the truth.
“Without hindrance” (ἀκωλύτως) indicates that there were no groups that stood in his way, as Paul had to deal with earlier in the book. Sometimes this rare word is used in legal contexts (P.Oxy 502, Ant. 12.104, 16.41, for example). The word might be used to describe some legal constraint, you cannot do want you want to because of a legal ruling (think of a restraining order in contemporary culture).
If we read the whole book of Acts, we might see quite a bit of “restraining” going on, things hinder the progress of the Gospel from the very beginning of Paul’s ministry. Jews in Asia Minor actively work against him on the first missionary journey, attack him publicly and stone him at Lystra, and continue to harass him when he returns to Jerusalem in the late 50s.
While Rome does not actively hinder Paul’s mission, he was in Roman custody several times in the book: at Philippi, nearly so at Thessalonica, he was arrested in Corinth, and was likely under arrest at some point in Ephesus, he cause a riot there as well. When he finally returned to Jerusalem he was taken into protective custody by Rome, but held for two years in Caesarea before being shipped to Rome, where he is under house arrest (at his own expense) for two years.
We might also add a kind of spiritual hindrance to this list as well. For example, Paul was forced to leave Thessalonica and was unable to return to the city, although he wanted to. In 1 Thess 3:18 he says that “Satan blocked our way,” literally “Satan tore up the road” so that Paul could not return and finish his work in the city. What happens in Corinth and Ephesus can also be taken as spiritual warfare, Satan was actively hindering Paul’s mission.
The book ends by telling us nothing is restraining the gospel. Paul is not hindered in the least by his imprisonment and there is nothing Rome can do to stop the gospel from going “to the ends of the earth.”