They are not tongues of fire. They looked like fire. If you read a more modern version, it becomes clearer. The meaning is that the "fire" divided and settled on each of them individually.
When Jesus received the Holy Spirit at His baptism, it came in the form of a dove. Jesus came as the suffering servant, to be crucified and save the human race from their sins - if they will receive Him. The apostles received power to be witnesses to the resurrection of Christ and to preach the Kingdom of God. In the Bible, "fire" mostly represents judgement and cleansing. The apostles were frightened and scattered after the death of Christ. Once they were baptised in the Holy Spirit, they were fearless and bold.
Thanks Gideon300 for your response. Your response is the closest to my view of the coming of the Holy Spirit in this case. While it is true that the fire is not actual fire, but only "like as of fire ", the term 'fire' is still used and so has meaning, just as the 'form of a dove' did in your reference. I see the fire as being a picture of Christ's sacrifice. We read: "an offering made by fire, of a sweet savour unto the LORD. ". This sacrifice scripture is an Old Testament picture of Jesus' sacrifice on the cross. When the Holy Spirit comes, it enables believers to speak of Christ's sacrifice on the cross. Thus, fire is referenced, in my opinion.
I see the term cloven as also having meaning. I see this as pointing to the fact that the gospel has two sides, salvation or condemnation. As the believers witness by the Holy Spirit about Christ's sacrifice, the gospel speaks of salvation for those that believe, and of condemnation for those that reject Christ. It is a bit, in my opinion, like those who rightly divide the word of truth. It is interesting that by and large the cloven-toed animals in the Old Testament were clean, whilst one-toed animals were unclean. So, I suppose this points to the gospel and having this two-sided component, like the double-edged sword. Similarly, John the Baptist ate locusts and wild honey. This, in my opinion, also shows the two sides of the gospel, with locusts being a picture of judgment, and honey as being a picture of salvation.