For testify or witnesses in Acts 1:8, the word martus
is used. First of all, witnessing means that you tell the facts that you have seen, like e.g., in a court case. Witnessing also means that you tell the truth, that Jesus of Nazareth was truly crucified, rose again, and ascended into heaven. This testimony requires faith and is met with much resistance.
The Holy Spirit is the driving force behind the witnesses. The apostles are the first witnesses, they received the news firsthand. When we witness today, it comes from the umptieth person.
But it is the same truth about Jesus and the same Spirit who gives courage and power to witness.
In Acts we often meet the witnesses: Peter gives a testimony (Acts 2:40, Acts 10:42) and later Paul to the Jews in Corinth (Acts 18:5), at the farewell from the elders in Ephesus (Acts 20:21) and in Rome (Acts 23:11 and Acts 28:23). Also, in Acts 8:25 we read: they had testified and spoken the word of the Lord
(dia-martureo).
25 Now when they had testified and spoken the word of the Lord, they returned to Jerusalem, preaching the gospel to many villages of the Samaritans.