"Various kinds of tongues" is a translation of two Greek words: genos glossa. The first word literally means kin, as in kindred or family. And the second means tongue, by implication a language, and specifically the language of one's kin (family). The Greek Lexicon expands the definition to mean the language or dialect used by a particular people distinct from that of other nations. So a literal translation might be "kindred languages," and again it suggests the language of one's kin or family, the language spoken by one's parents, one's native tongue. It is an untenable stretch of the imagination to think that it means unknown languages of any kind.
In the light of our previous discussion of tongues, we find that this gift of "various kinds of tongues" is about speaking the gospel in the native tongue(s) of believers in order to share it with one's family at home. Remember that the purpose of tongues is to bring the gospel of Jesus Christ to the nations, to the Gentiles, to the people of the world. Through Christ the gospel of the God of the Hebrews was exported to the world in the native tongues of the various nations.
Paul's mention of this gift is a repetition of 1 Corinthians 12:10, and biblical repetition serves to emphasize importance. Various kinds of tongues would serve the expansion and dissemination of the gospel to the world. Paul was not instructing disciples to speak in languages they didn't know, nor in forgotten languages, nor to speak in languages known only to God. Rather, he was instructing disciples to take their knowledge, experience and love of the gospel of Jesus Christ and share it with their family and friends at home, in their native countries, in their native tongues, as a means of evangelizing the Gentiles, non-Hebrews.
This gift, rather than being a fanciful flight into realms of so-called higher spirituality, was the most common, ordinary thing imaginable. Because the gift of tongues that was given in Acts 2 was the gift of speaking (and writing) the gospel of Jesus Christ in non-Hebrew languages for the sake of world evangelization, this repetition of that gift simply emphasizes its importance. Paul was acknowledging that foreigners, Gentiles, had indeed received God's grace of salvation and the power of the Holy Spirit, and was directing and empowering those Gentile Christians to take the gospel to their homelands and to do so in their own native languages.
The application for us is the same now as it was then. Christians everywhere are directed and empowered to share their faith in Jesus Christ in any and every language, but particularly to do so in their most common and familiar language they know. Sharing the gospel in one's native tongue by a true believer will do much to alleviate the difficulties that accrue to those who try to translate it into a language that is not their own native tongue. In short, the biblical gospel of Jesus Christ escaped the confines of the Hebrew language as Gentile Christians carried it home in their native tongues. And this has been a great gift of the Spirit, a continuing gift. In fact, this gift will continue into eternity because sharing the love of Jesus Christ is at the heart of the gospel.