ezoolander,
A lot of people who believe in speaking in tongues think of it as a special way to pray better. I don't think that the Bible really supports this view. It might be true. But the verse they used to support it, from Romans 8, says that the Spirit intercedes with 'groanings that cannot be uttered' when we don't know how to pray. But tongues were spoken 'as the Spirit gave them utterance.' Tongues can be uttered.
I Corinthians 14 shows that the one who speaks in tongues speaks mysteries with his spirit, and that he edifies himself. If he prays in tongues, 'he gives thanks well, but the other is not edified.' Paul spent much of the chapter building up a case for the importance of interpreting speaking in tongues instead of just speaking in tongues in church without interpreting.
As for what speaking in tongues is, I don't think real speaking in tongues is just gibberish. I wouldn't assume that everything that passes for speaking in tongues is the genuine article, but I don't see any warnings in the Bible that we should be on the lookout for false speaking in tongues, so I try not to be too judgmental of people's experiences in this regard.
There were some different movements that experienced speaking in tongues throughout history, especially in the 1800's, but it started to become more prominent with the start of the Pentecostal movement. American Pentecostals will often trace the movement to 1901 in Topeka Kansas, and say it spread greatly from the Azusa Street revival in Los Angeles around 1906 to 1908. I have read and heard (an old interview) several references to people going to the meetings at Azusa Street and either hearing their own languages, Russian, Japanese, etc. "in tongues." There was also a book in the early 70s that contained several accounts of this. Sometimes the native speaker could verify the interpretation in English. I've never witnessed that.
I recently read an article by a missionary to Hong Kong and China, Dennis Balcom, in which he wrote of hearing Chinese villagers speak in tongues in English. His daughter and son-in-law are supposed to visit my church here before too long. I heard one of the denominational officials of the Assemblies of God talk about a fellow missionary who preached in tongues when his interpreter wasn't present. I also knew a missionary who had an urge to speak in tongues while doing a crusade among the Cherokee. Someone asked him afterwards how he could speak in Cherokee. He had rebuked some youths who were trying to do some mischief, maybe cut tent cords or light fire crackers under the stage. I think it was fireworks. It scared them off.
I have a degree in Linguistics and I've traveled quite a bit overseas. I've heard speaking in tongues before where I didn't know if the person was speaking in a regional language while praying until the interpretation came, and I realized it was speaking in tongues. I've heard Americans speaking in what to me sounds like foreign languages. Someone on a Facebook forum posted a recording that is allegedly of a Polish girl praying 'in tongues' in English. It's on YouTube somewhere. A German Church of God pastor knows two Europeans who speak in tongues in English. I tried to friend one of the guys. He doesn't know English, but the German pastor says he speaks in tongues in KJV English. He knows of another person who speaks in tongues in English.
As far as interpretations go, I have had a couple of friends who have experienced getting an interpretation to a tongue, but someone else gave the same thing before they could. One was a friend at a Christian school in middle school and the other was a college roommate of mine when I lived in a dorm. I haven't experienced that. But I know something similar happens with prophecies. I don't usually get long prophecies, but I've gotten several dozen words of knowledge. I've had the experience where I got a word of knowledge for someone, but before I could share it, someone prophesied the same thing over the person. I've also gone to one place, someone prophesied over me, and gone elsewhere, and someone else prophesied the same sort of things. It's not like all the prophecies are really generic either. One year, I'd get a few prophecies encouraging me in one area, and another year, get prophecies encouraging me in another area. I've seen this happen to other people, too. Prophecies and words of knowledge can be extremely detailed, to the extent that they are obviously supernatural. They can also say things the person delivering them wouldn't naturally know. One that sticks out in my mind was where a guy got a word of knowledge for some teens he'd just met and prayed that their friend Toby wouldn't drive so wrecklessly. Just about every American teen has a friend whose a reckless driver, but how many have a friend named Toby?