How does Gibbon define "good" or "bad" emperors in his book, and what do his portrayals of various emperors suggests about his views on government and politics?

I am going to assume that you are referring to Edward Gibbon and his 1776 work, The Decline and Fall of the Roman Empire.
Gibbon’s definition of a good emperor comes through most clearly in his discussion of what is referred to as the “Age of the Five Good Emperors.” This encompasses the period from 96–180 CE and includes the reigns of Nerva, Trajan, Hadrian, Antoninus Pius, and Marcus Aurelius. Gibbon describes this period in chapter 1 of his work in the following way:

In the second century of the Christian Aera, the empire of Rome comprehended the fairest part of the earth, and the most civilized portion of mankind. The frontiers of that extensive monarchy were guarded by ancient renown and disciplined valor. The gentle but powerful influence of laws and manners had gradually cemented the union of the provinces. Their peaceful inhabitants enjoyed and abused the advantages of wealth and luxury. The image of a free constitution was preserved with decent reverence: the Roman senate appeared to possess the sovereign authority, and devolved on the emperors all the executive powers of government. During a happy period of more than fourscore years, the public administration was conducted by the virtue and abilities of Nerva, Trajan, Hadrian, and the two Antonines.

This description is very suggestive of his views on government and politics. Notice what he focuses on: the status of Rome’s frontiers and military, law and order within the empire, the power of the Senate and its relationship with the emperor in power, and the state of the bureaucracy. In Gibbon’s view, the five “good” emperors did well in all of these arenas. During their reigns, the empire’s borders and military were secure and well maintained (sometimes even extended), the bureaucracy functioned well, trade and agriculture flourished, and the government took care of its subjects through things like public works.
Nerva, for example, was known for consulting the Senate and halting various persecutions, including returning confiscated property. Trajan was a distinguished military commander whose victories extended Rome’s borders. He also maintained the bureaucracy and engaged in public building. Hadrian did the same, building the famous Hadrian’s Wall to secure Rome’s northern frontier. Antoninus Pius was known for maintaining Roman tradition and keeping the peace. Marcus Aurelius successfully waged war against and defeated the Germans and the Parthians, and further expanded and secured Rome’s borders. So, all of these emperors had some elements of Gibbon’s ideal of a good emperor. Gibbon devotes his first three chapters to what he sees as this golden age of good emperors.
Gibbon also claims that the age of the good emperors ended with Marcus Aurelius’s death and that Rome then began to decline and fall. This is mostly because it began to be ruled by bad emperors, to whom he devotes the rest of the chapters of his work (starting with chapter 4). He begins by eviscerating Marcus Aurelius’s son, Commodus, one example of a bad emperor. He writes that

The monstrous vices of the son have cast a shade on the purity of the father’s virtues. It has been objected to Marcus, that he sacrificed the happiness of millions to a fond partiality for a worthless boy; and that he chose a successor in his own family, rather than in the republic...but these motives will not account for the unprovoked cruelties of Commodus, who had nothing to wish and everything to enjoy. The beloved son of Marcus succeeded to his father, amidst the acclamations of the senate and armies . . . Nature had formed him of a weak rather than a wicked disposition. His simplicity and timidity rendered him the slave of his attendants, who gradually corrupted his mind. His cruelty, which at first obeyed the dictates of others, degenerated into habit, and at length became the ruling passion of his soul.

As you can see, Gibbon makes it a point to note that Commodus was chosen by Marcus Aurelius as his successor because he was his son, not because he was qualified. In other words, he was not really worthy or deserving of the title, and he proved this during his reign by being cruel, weak, and selfish and not caring about the republic. We get a hint of Gibbon’s own thoughts on dynastic politics and government, because he implies that emperors should be chosen for the good of the republic and with the approval of the Senate, based on their merit rather than their parentage. I would recommend checking out chapter 4 and those following it for more examples of "bad emperors."
https://books.google.com/books?id=FXllDwAAQBAJ&lpg=PP1&pg=PP1