Speaking in tongues is mentioned in several passages in the New Testament: Mark 16:17; Acts 2:1-13; 10:44-46; 19:6; 1 Cor 12-14. It is important to understand that the Greek word for “tongue” was the same word used for “language”, so “speaking in tongues” means “speaking in languages”.
The reference in Mark 16:17 is to speaking in “new tongues”, which may mean languages previously unknown to the apostles.
In Acts 2 the reference is clearly to human languages, with many different peoples hearing the apostles in their “own tongues” (v11).
Acts 10:44-46 is uncertain; speaking in tongues is a sign of the pouring of the Holy Spirit but we are not told whether they spoke human languages or something else. The same is true of Acts 19:6.
In 1 Corinthians 12-14 we have the fullest account of speaking in tongues. When writing about speaking in tongues Paul compares it with speaking a foreign language: “if I do not know the meaning of the language, I shall be a foreigner to him who speaks” (14:11). He also commands that if they are to speak in tongues in the church then there should be an interpreter present (14:27-28), which implies that languages were being spoken that could be interpreted.
This being said, there are some other aspects to speaking in tongues. Paul refers to speaking with the tongues “of angels” (13:1) and says that one who speaks with a tongue “does not speak to men but to God” (14:2). However we should be cautious about reading too much into these statements.