The idea of "teenagers" being a distinct stage of life seems to be a 20th century culture phenomenon. Where did the idea come from? Was it a creation of the popular media, or a reflection of an already-existing change in social development?

It would be more accurate to say the concept of "teenager" or "adolescence" must be historicized: it has meant different things at different times. I've talked earlier on AH about the western medieval side of things.:

n.b. This piece of writing is apparently brought to you by my first full month writing on AskHistorians...wow...

Later medieval England certainly recognized adolescence as a distinctive life stage in practice. Of course there were exceptions of kids having to "grow up too fast," but unfortunately those exist today, as well. To bust open one myth first: no, medieval kids weren't always married by age 12, although it occasionally happened. In short: girls tended to marry earlier than boys, upper class girls in particularly tended to marry earlier than lower and middle class ones, and marriage age crept upward over the course of the later Middle Ages. Urban Renaissance Italy is the most famous case of girls systematically marrying quite young. At the same time, it's important to recognize that medieval teenagehood was more akin to a blend of adulthood and childhood, and direct preparation for adult life, than we perhaps think of it in the modern West.

Among rural and urban peasants in late medieval England, there is ample evidence for teenagehood as a distinct life phase for girls and boys. Teenagers spent a lot of their time working alongside adults, but also some of their time working and playing with other children. For example, younger teenage boys did not compete in organized adult games like archery and wrestling. They spent time in the fields and workshops with their fathers, but unlike adult men, they continued to participate in fishing and gathering with younger children and teenage girls.

Especially towards the end of the Middle Ages into the early modern era, peasant girls in particular (to some extent boys as well) often spent their teenage years as domestic servants. On one hand, this was good training for their futures running their household; on the other, it helped girls build up a good dowry for their financial future after marriage.

For boys in particular intending to pursue a trade, the guild structure also created distinct social statuses that separated the men from the boys quite literally (and in a few cases girls, although women guild members were most often widows of deceased male members carrying on in their stead). One of the best demonstrations of the social aspects of this is actually university students (universitas originally referring not to the school but to the guild of its members). Urban chronicles often rail against the ruckus caused by student hooligans! (Sometimes they were exempt from civic regulations, even, thanks to the power of their universitas.)

The emotional aspects of adolescence weren't ignored, either. Some villages actually institutionalized flirting. Croscombe had a Maidens' Gild and their male counterpart Younglyngs as social-religious groups. On alternate celebration days, each gild would blockade part of the village and exact a toll from members of the other as a fundraiser.

For the nobility, I mostly know the female side of the story. Here, a lot of the emphasis was on parents and daughter cooperating (well, ideally) to secure her the best marriage possible. A lot of this involved helping the teenage daughter develop good social contacts through parties, court events, letter writing...and, like their peasant counterparts, frequently spending her teenage years away from her parents' home.

In some cases, this ended up as varying degrees of domestic servitude; in others, girls ended up basically as surrogate daughters, or could even be formal ladies-in-waiting at a noble court. You might think of Anne Boleyn, who was offered a place in Margaret of Austria's court (in the Netherlands) in 1513 and then subsequently at the French royal court. Noble girls needed a different set of household management skills from their peasant counterparts, and they'd also spend these years learning and using courtly arts (dancing, fine sewing, manners).

As for the "end of adolescence," I think a fair case can be made for marriage as the chief marker. Looking at cases of moneyed orphans who were wards of the state, courts would grant them their inheritance, held in trust, upon marriage. In Renaissance-era Italy, the very few women whose fathers arranged a humanist education for them tended to be literary fountains during adolescence--and then shift their creative efforts upon marriage to writing letters to their adult children. (This is not a universal story, but it's sadly common.) One of the reasons the marriage age for men in late medieval Italy was so late, was their desire not to inherit money too early and risk breaking up the family patrimony. The other possibility specific to women would be childbirth. Although women in certain social categories married earlier, even with queens and duchesses, average age at first childbirth tends to hover around 18-20.

One interesting note on that point. I mentioned earlier that the most entrenched case of early marriage for girls was urban Italy. Christine Klapisch-Zuber argues that a big effect of this practice was the new wife's lack of social power within her new family, since upper class women literally married into their husband's paterfamilias--frequently moving into her father-in-law's house. Thus, even a newly married teenage girl would have had a period of time learning the skills of urban household management before her husband came into his patrimony and his own household for her to run.