It is a supernatural phenomena in which one speaks a language he or she does not know or understand but which God understands perfectly.
Not all Christians subscribe to speaking in tongues (it's not required). Some believe that it happened on the day of Pentecost in the upper room but not today.
I happen to believe it still exists today. Here is some scripture about it. I hope it helps:
1 Corinthians 14:1-4
(NLT)
Tongues and Prophecy
1 Let love be your highest goal! But you should also desire the special abilities the Spirit gives—especially the ability to prophesy. 2 For if you have the ability to speak in tongues,[a] you will be talking only to God, since people won’t be able to understand you. You will be speaking by the power of the Spirit, but it will all be mysterious. 3 But one who prophesies strengthens others, encourages them, and comforts them. 4 A person who speaks in tongues is strengthened personally, but one who speaks a word of prophecy strengthens the entire church.
5 I wish you could all speak in tongues, but even more I wish you could all prophesy. For prophecy is greater than speaking in tongues, unless someone interprets what you are saying so that the whole church will be strengthened.
14-15
14 For if I pray in tongues, my spirit is praying, but I don’t understand what I am saying.
15 Well then, what shall I do? I will pray in the spirit,[d] and I will also pray in words I understand. I will sing in the spirit, and I will also sing in words I understand.
39-40
39 So, my dear brothers and sisters, be eager to prophesy, and don’t forbid speaking in tongues. 40 But be sure that everything is done properly and in order.