What does it mean to “speak in tongues”? Most would likely say “tongues” are languages that are unknown to the human race, and that only God (and perhaps angels) can understand. But they would be wrong. The first thing we must understand is that the word “tongue” is simply a synonym for “language.” Thus, to “speak in tongues” simply means “to speak in languages.”
Now, in the New Testament, “tongue speaking” was simply the miraculous ability to speak an actual, intelligible, human language which the speaker had never learned by natural processes. For instance, if someone came to me earnestly desiring to be taught the truth of the gospel, but who spoke no English, we would be in a dilemma—I would not be able to teach them God’s word! The apostles and prophets were going to find themselves in that very dilemma in the church’s infancy; so God—via the Holy Spirit—granted them the ability to speak languages they did not otherwise know, in order to bypass any potential language barrier.
We can read about the first occurrence of “tongue-speaking” in Acts 2: the apostles were filled with the Holy Spirit, and “began to speak in other tongues” (v. 4). Notice that they were speaking in “other tongues”—i.e., tongues other than their own native tongue (language)! Notice also that the bystanders said the apostles were speaking “in our own native language” (v. 8). What were the apostles doing? Speaking “in tongues;” but what were they speaking? The representative native languages, which was understood by those present. They were speaking actual human languages, by the power of the Holy Spirit.
Clearly, to “speak in tongues” was not some overpowering influence of the Holy Spirit causing people to speak some “heavenly” language that was unknown to all but God Himself, but was nothing more than the miraculous ability to speak in another human language (e.g., Greek, Spanish, German, Russian, etc.). As such, now that we have the written word of God in virtually every conceivable language, “speaking in tongues”—along with all other miracles—is no longer needed, and thus does not exist today (cf. 1 Cor. 13:8-10).