The significance of Acts 1:8 is multilayered. It is a promise of heavenly power to the Apostles and is a blue print to the book of Acts. The surrounding text of Acts 1:8 helps us to understand what Luke is telling us. The text before the 8th verse has the disciples asking if Jesus would restore the kingdom to Israel. The timing of the kingdom was within the sovereign purposes of God, not to be known by the apostles. It is clear that knowing the time would not have been beneficial to them. What was within their realm of responsibility was to proclaim the good news of the gospel to all nations, and thus our Lord reiterated the Great Commission, not so much as a command, but as a prophecy of what was certain to come. The Holy Spirit would come upon them, bestowing power on them, and they would be witnesses to the nations. Acts is the historical account of how, in the wisdom of God, this was accomplished in spite of His disciples, as well as because of them. We do use this passage in the modern church to promote missions and community outreach and it can be used this way correctly. This passage also serves as a blueprint for the book of Acts; the witness of the disciples starting in Jerusalem and in all Judea, and Phillip (and others) went to Samaria, and Paul was the witness to the “remotest part of the earth (NAS)” when he went to Rome. Thus the reason Luke concluded Acts with Paul having arrived in Rome awaiting his trial.
Jesus promised the gift of the Holy Spirit to the disciples and to all believers after His ascension. This is a similar promise made in John 7:37-39 where Jesus said, “On the last day of the feast, the greatest day, Jesus stood up and shouted out, “If anyone is thirsty, let him come to me, and let the one who believes in me drink. Just as the scripture says, ‘From within him will flow rivers of living water.’ (Now he said this about the Spirit, whom those who believed in him were going to receive; for the Spirit had not yet been given, because Jesus was not yet glorified.).” In Acts, the term power appears ten times referring to miracles or other effects of power and the enablement in word and in action. In Acts 1:8, Jesus is telling His disciples and us Christians that the Holy Spirit empowers them and us to be His witnesses.
The book of Acts is sometimes called “The Acts of the Apostles,” but a more accurate title would be “The Acts of the Holy Spirit.” The Holy Spirit is the One who acted through the Apostles. Whenever a miracle happened, the miracle gave power to what the Apostles were preaching; Jesus alone for salvation. The first miracle done after the Holy Spirit came to the Apostles was at Pentecost .
The tongues spoken at Pentecost were not the “heavenly language.” The adjective Luke uses (heteros in the Greek) when he says, “they began to speak with other tongues.” simply means languages different from the normal language they were used to speaking. Based on Acts 2:7-8 (And they were all amazed and marveled, saying one to another, Behold, are not all these which speak Galileans? And how hear we every man in our own tongue, wherein we were born?), the crowd was surprised to hear the Apostles speaking their language. The word “language” in Acts 2:6 is the translation of dialekto from which our word “dialect” comes. The two words glossa (tongue) and dialektos (language) are used synonymously, making it obvious that the Apostles were speaking in known languages other than the language native to them; the languages are then identified in verses 9-11. The languages spoken at Pentecost were regular languages. The miracle is that these are languages the Apostles didn’t know before they took the stage. Because the languages were spoken via the Holy Spirit, it gave power to what the Apostles were saying so 3,000 people accepted Jesus Christ as Savior.
 Robert L. Deffinbaugh, “Getting Ahead of God (Acts 1:1-26),” Bible.org, August 12, 2004. https://bible.org/seriespage/1-getting-ahead-god-acts-11-26
 “What does Acts 1:8 mean: “when the Holy Spirit has come upon you”?,” Bible.org, last modified January 1,2001. https://bible.org/question/what-does-acts-18-mean-%E2%80%9Cwhen-holy-spirit-has-come-upon-you%E2%80%9D
 Darrell L. Bock, Acts. (Grand Rapids, MI: Baker Academic, 2007), 63.