Boldness in speech (παρρησιάζομαι) is to clearly speak a word openly.
After Paul’s conversion to Christianity and three years in the desert learning from Christ to serve as the steward of the dispensation of grace, he returned to Damascus, speaking clearly and openly, with boldness of speech, showing from Scripture that Jesus is the Messiah, Acts 9:27.
While Paul and Barnabas were in Antioch of Pisidia sharing the gospel of the Christ in the synagogue, the Jews were filled with envy because of the great multitude of Gentiles following Paul; therefore, they began to speak falsely against and oppose what Paul was saying. Their attempt to thwart the good news Paul declared to them only caused Paul and Barnabas to grow in the openness and clarity of their speech, telling the Jews since they did not desire to follow God and counted themselves as unworthy to receive enteral life, they would turn to the Gentiles, Acts 13:46.
In Ephesus, when Apollos, a man from Alexandria, spoke accurately concerning the things of the Lord, knowing only the immersion of John the Baptist, as he began to speak openly in the synagogue, Aquila and Priscilla heard him. They then took him aside and filled him in on all that had happened since the immersion of John, more accurately explaining to him the way of God, Acts 18:26.
When defending himself against false charges from the Jew before Festus and Agrippa, after Festus called him mad, Paul spoke freely to King Agrippa because Paul was convinced that the King already knew about this matter, Acts 26:26. Because of his openness and clarity of words, Agrippa responded saying, “You almost persuade me also to become a Christian.” However, the matter at hand was if Paul was guilty. In response to Festus’ inquiry, Agrippa states that there was nothing Paul did to deserve being in chains; however, due to the Jews working out a plan with the authorities to allow them to kill him, he had appealed to Caesar, which was his right as a Roman. He, therefore, could not be released, Acts 26:32.
After going over the defense we have against Satan, Paul encourages the saints to worship God while supplication for other saints, including himself, so that he has openness and transparency in speech to make known what is the mystery of the gospel, for he is an ambassador in chains, Ephesians 6:20.
Boldness in speech comes from confidence in what is spoken based upon its truthfulness. Paul knew that he was speaking the truth; therefore, even when the Jews would speak against him and oppose what he was saying or beat him for talking about the death for sins and resurrection of Christ, he grew in openness and clarity of his speech because his confidence was in God, not men.