Power (dunamin). Not the “power” about which they were concerned (political organization and equipments for empire on the order of Rome). Their very question was ample proof of their need of this new “power” (dunamin), to enable them (from dunamai, to be able), to grapple with the spread of the gospel in the world.
When the Holy Ghost is come upon you (epelthontos tou hagiou pneumatos eph' humas). Genitive absolute and is simultaneous in time with the preceding verb “shall receive” (lēmpsesthe). The Holy Spirit will give them the “power” as he comes upon them. This is the baptism of the Holy Spirit referred to in Act 1:5.
My witnesses (mou martures). Correct text. “Royal words of magnificent and Divine assurance” (Furneaux). Our word martyrs is this word martures. In Luk 24:48 Jesus calls the disciples “witnesses to these things” (martures toutōn, objective genitive). In Act 1:22 an apostle has to be a “witness to the Resurrection” of Christ and in Act 10:39 to the life and work of Jesus. Hence there could be no “apostles” in this sense after the first generation. But here the apostles are called “my witnesses.” “His by a direct personal relationship” (Knowling). The expanding sphere of their witness when the Holy Spirit comes upon them is “unto the uttermost part of the earth” (heōs eschatou tēs gēs). Once they had been commanded to avoid Samaria (Mat 10:5), but now it is included in the world program as already outlined on the mountain in Galilee (Mat 28:19; Mar 16:15). Jesus is on Olivet as he points to Jerusalem, Judea, Samaria, the uttermost (last, eschatou) part of the earth. The program still beckons us on to world conquest for Christ. “The Acts themselves form the best commentary on these words, and the words themselves might be given as the best summary of the Acts” (Page). The events follow this outline (Jerusalem till the end of chapter 7, with the martyrdom of Stephen, the scattering of the saints through Judea and Samaria in chapter 8, the conversion of Saul, chapter 9, the spread of the gospel to Romans in Caesarea by Peter (chapter 10), to Greeks in Antioch (chapter 11), finally Paul’s world tours and arrest and arrival in Rome (chapter 11 to chapter 28).