It's very difficult to conceptualize the idea of adolescence, because it can be approached from various angles. From a biological perspective, it can be defined as the age where a person goes through major physical and psychological changes usually around the time of puberty. On the other hand, it can be defined as the time where a person is seeking emotional and mental maturity. However, this is where it gets slippery. Who gets to decide what is mature? It's hard to set a standard and make generalization when there are countless factors that contribute to maturity and immaturity. Although it might be an inefficient and rudimentary approach, these situations must be judged on a case by case basis. However, if I must explain the meaning of adolescence, I would say it is the time where a person begins to break free of the accepted theories imposed upon them by society and undertake the responsibility to behave and think as an individual.
In relation to teen angst, I believe that teen angst occurs when an adolescence is having a hard time shedding the status quo and discovering an identity as a separate entity. Additionally, finding one's place in society as a whole while maintaining a firm grasp on one's individuality can be- not an insurmountable obstacle- but an obstacle nonetheless. The term angst is a pre-cognate with the Latin term "angor" meaning "choking, clogging". I see a relation between teen angst and "choking" in that teen angst is caused by society trying to choke adolescence with its preconceived notions of right or wrong.