I was reading about Marcus Aurelius today and noticed the article states he was the last of the "Five Good Emperors." I started reading about them and don't see anything particularly special about them. They seem competent, and their reigns saw improvements to Rome, but they don't really seem all that special to me. Is it a context thing? Were the other Emperors immediately before and after them just that bad? What am I missing here?
Machiavelli calls them this in the first book of his Discourses (1.10):
"...perché tutti gl'imperadori che succederono all'imperio per eredità , eccetto Tito, furono cattivi, quelli che per adozione, furono tutti buoni come furono quei cinque da Nerva a Marco."
"...because all the emperors that rose to command through inheritance, except Titus, were bad, [but] those that did so through adoption were all good, as were those five from Nerva to Marcus Aurelius."
IIRC, that's the first example of this classification, and it certainly predates Gibbon (with whom it was very popular). In terms of what they actually did to earn the title, I think you've got the sense of it pretty well - they just happened to not be as "bad" as the emperors immediately before/after them, and they got picked up by later authors as exemplary for it.
Nerva was a weak Emperor, but he made the important decision to appoint an heir instead of having it be hereditary. He chose a very successful & popular General named Trajan (Marcus Ulpius Traianus) as his heir.
Trajan was by all accounts a very 'good' man in comparison to many other Emperors. He refused to have senators executed just because someone else claimed they were disloyal, he increased aid to the poor, and he attempted to appoint qualified governors over the provinces. At his death in 117, the Roman Empire covered its largest area.
I'll let others answer about Hadrian, Antoninus Pious, & Marcus Aurelius.
Source: I did thesis work on Trajan 20 years ago. Much of this info is in A Dictionary of the Roman Empire by Matthew Bunson. Dio wrote about Trajan as well.