‘Speaking in tongues’ is a term generally used today for glossalalia, a practice in Pentecostal churches. Glossalalia is not a real language but strings of broken phonemes of languages known, or at least heard by, the speaker.
In the New Testament ‘tongues’ (Greek glossai) is simply the normal Greek word for languages. In most incidents in the New Testament a ‘tongue’ is simply Hebrew, Greek or a similar local language.
However the ‘tongues’ in 1 Corinthians 14 do not seem to be normal languages but something else:
2 For anyone who speaks in a tongue does not speak to people but to God. Indeed, no one understands them; they utter mysteries by the Spirit. (I Corinthians 14:2 NIV)
For this reason at the end of this chapter Paul counsels the Corinth church to not allow this practice unless these utterances are translated.
Otherwise in the Book of Acts ‘tongues’ means ‘speaking in another language of the world’. We can see this in Acts 2:4-11, where the disciples first started speaking in tongues:
{4} … they [the disciples] were all filled with the Holy Spirit and began to speak in other tongues as the Spirit gave them utterance. {5} Now there were dwelling in Jerusalem Jews, devout men from every nation under heaven. {6} And at this sound the multitude came together, and they were bewildered, because each one was hearing them speak in his own language. {7} And they were amazed and astonished, saying, “Are not all these who are speaking Galileans? {8} And how is it that we hear, each of us in his own native language? {9} Parthians and Medes and Elamites and residents of Mesopotamia, Judea and Cappadocia, Pontus and Asia, {10} Phrygia and Pamphylia, Egypt and the parts of Libya belonging to Cyrene, and visitors from Rome, {11} both Jews and proselytes, Cretans and Arabians—we hear them telling in our own tongues the mighty works of God.”