Easton's Bible Dictionary defines a vision as a vivid apparition, not a dream. In plain English it is a visual message from God. I like to imagine that it's a bit like the holographic messages in Star Wars but that is entirely from my imagination and not the Bible. Visions are one way God communicated with his people in both the Old and New Testaments. He used visions to warn people of coming events, to encourage them, to warn people of their disobedience, or to instruct someone what to do. Visions are different to dreams as they can occur while you're awake.
I am fairly certain that God still speaks to people in visions but I think that most of us are too busy to be receptive. In the passage in Acts 2 it was the Day of Pentecost when the Holy Spirit came on the disciples. Peter was quoting a passage from the book of Joel in the Old Testament.
This is what I will do in the last days, God says:
I will pour out my Spirit on everyone.
Your sons and daughters will proclaim my message;
your young men will see visions,
and your old men will have dreams.
My understanding is that we are in those last days now (that is, the time between Jesus' first coming and when he will come back again. I don't think Peter was implying that only men will have visions and dreams but that men and women will proclaim his message, see visions and have dreams. He was saying that the Holy Spirit would be poured out on everyone regardless of race or gender.
Short and sweet inspirations for Christian teen girls.