One might say that it is adding information to the noun lesson. Grammatically, syntactically, that's what it's doing. It is an adjectival phrase applied to that noun.
However, it's actually much more important to the meaning of the sentence than the word lesson.
It might be rephrased as
What happened next was astonishing, and taught a lot about developing an emotionally charged event.
So, yes, it's an adjectival phrase, but don't let that minimise its semantic importance.
You might or might not already appreciate this, but for the benefit of other site users, I just wanted to point out how this is a very good example that sometimes the principal verb (here offered), and subject and object nouns, contribute a lot less to the substance of a sentence than a prepositional phrase, an adverbial, or various other less-grammatically-essential elements.