What does it mean to "prophesy"?

“ ‘And in the last days it shall be, God declares, that I will pour out my Spirit on all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams; even on my male servants and female servants in those days I will pour out my Spirit, and they shall prophesy’ ” (Acts 2:17-18).

In his book, The Acts of the Risen Lord Jesus, Alan J. Thompson provides some great insight into the meaning of prophesy in the context of Acts 2. He writes,

What does it mean to ‘prophesy in this context? The passage cited by Peter particularly stresses the activity of the Spirit on ‘all’ of God’s people. The emphasis on ‘all’ of God’s people receiving God’s Spirit was already hinted at earlier in Acts 2 in verses 3-4. What looked like tongues of fire came to rest on ‘each of them’ and ‘all of them were filled with the Spirit’. Peter states that this is what Joel spoke about: a time in the last days when God will pour out his Spirit on ‘all’ of his people (Acts 2:17). This emphasis on the totality of God’s people is then filled out in three groups which highlight the fact that there will be no distinction in age or gender among the people who receive God’s Spirit: ‘sons and daughters…young men and old men…servants, both men and women’. It is all of God’s people who are said to ‘prophesy’ here. The difficulty, however is that in Acts itself only a select few are said to be ‘prophets’ (Acts 11:27; 13:1; 15:32; 21:10) and the activity of ‘prophesying’ is rare (Acts 19:6; 21:9). The act of ‘prophesying’ in Acts 2, therefore, must be understood within the context of what Peter says in this quotation from Joel. That is, that there is a broader sense of the word in which all of God’s people ‘prophesy’. In contrast to the work of the Spirit in the OT when the Holy Spirit empowered only certain people, prophets, to mediate God’s word to the people, now all of God’s people are able to speak for God. Although not explicitly cited by Peter, it appears Moses’ hope is being fulfilled: ‘I wish that all the LORD’s people were prophets and that the LORD would put his Spirit on them’ (Num. 11:29). Now that the Spirit has come and God’s saving promises have been revealed in Christ, all of God’s people are enabled by his Spirit to announce the fulfillment of God’s saving plan and promises when they proclaim Christ. The ‘least in the kingdom of God’ is greater than John the Baptist (Luke 7:28).1 

1 Thompson, Alan J. "God's Empowering Presence." The Acts of the Risen Lord Jesus: Luke's Account of God's Unfolding Plan. Nottingham, England: Apollos, 2011. 131. Print.