Quote 1
POPE ADRIAN
Lord Cardinals of France and Padua,
Go forthwith to our holy consistory
And read amongst the statutes decretal
What, by the holy council held at Trent,
The sacred synod hath decreed for him
That doth assume the papal government
Without election and a true consent. (3.1.102-108)
Here, Pope Adrian charges his cardinals with determining a punishment for Bruno, a Saxon man who has been declared pope by the German emperor. The Council of Trent was a meeting of bishops and cardinals that occurred every once in a while between 1545 and 1563 as a response to the challenges of the Reformation. Throughout the medieval period, the Catholic Church had all kinds of problems, the most common of which were divisions within the Church that occurred when people couldn't agree upon a Pope. The character of Bruno is supposed to be the product of one such a division.
Quote 2
POPE ADRIAN
Pope Julius did abuse the Church's rights,
And therefore none of his decrees can stand.
Is not all power on earth bestowed on us?
And therefore, though we would, we cannot err. (3.1.149-151)
Bruno has claimed that one of Pope Adrian's predecessors, Julius, recognized the Holy Roman Emperor as his lord, which is so not cool in Adrian's book. But in his response, Adrian contradicts himself, which doesn't make his argument look so sound. First, he says that Julius's decrees were invalid because he gave the Church too much power. Then he's all, "the papal office is infallible" (unable to make a mistake). But wait—if the papal office is infallible, how could Pope Julius's decrees have been invalid? This guy, like Faustus, could have used a logic class or two.
Quote 3
POPE ADRIAN
Behold this silver belt whereto is fixed
Seven golden seals, fast sealed with seven seals,
In token of our seven-fold power from heaven,
To bind or loose, lock fast, condemn or judge.
Resign or seal, or what so pleaseth us.
Then he and thou and all the world shall stoop,
Or be assured of our dreadful curse
To light as heavy as the pains of hell. (3.1.153-160)
Pope Adrian's Catholic Church believed that Jesus gave the Pope the power to save and condemn souls. That means that, when it comes down to it, the decision to either forgive a sinner or kick him out of the Church altogether (a practice called excommunication) was with the Pope. To gain the Pope's forgiveness, folks would buy indulgences, or forgiveness for sins. Many folks felt that this practice amounted to nothing more than people buying their tickets to heaven, to put it bluntly, and this practice was one of the main things that members of the Protestant Reformation objected to when it came to the Catholic Church. This passage shows the Pope using the power to save or condemn souls in just the way the Reformation claimed it did—to gain power, and make all the world "stoop."