What happens in Canto XIX of Dante's Inferno?

Canto XIX
Having passed the second pouch of excrement-encrusted flatterers, the poets carefully step down even lower into the Eighth Circle where they witness the worst punishment yet inflicted on sinners. These condemned souls are the Simonists, clergy who had sold indulgences, that is, money paid to priests that supposedly absolved people of their sins or paid for other special amenities in Heaven. Dante’s disgust with these fraudulent friars is unrestrained. He admonishes them saying that they prostituted themselves for money:

“O Simon Magus, O forlorn disciples,
Ye who the things of God, which ought to be
The brides of holiness, rapaciously
For silver and for gold do prostitute,
Now it behoves for you the trumpet sound,
Because in this third Bolgia ye abide.
We had already on the following tomb
Ascended to that portion of the crag
Which o'er the middle of the moat hangs plumb.
Wisdom supreme, O how great art thou showest
In heaven, in earth, and in the evil world,
And with what justice doth thy power distribute!”

Dante begins his invective by calling out Simon Magus, for whom all Simonists are named. In the Bible, Simon is a man who uses witchcraft (a “magus”). The story of Simon and the apostles can be found in Acts 8:9-24. After witnessing two of Jesus’s disciples, Peter and John, perform miracles, Simon Magus is so impressed that he asks Peter to teach him how to do the same...for money. Indignantly, Peter chastises the magician, insulted that he believes the gifts of Christ could be purchased. There is a more detailed story about Simon Magus’s clash with Peter in The Acts of Peter. (This story is recorded in one of the books known as the “apocrypha.” These books were written around the same period as the Bible and have many similiarities, but for various reasons, were not canonized by early Christians and are not included in the Bible proper.)
In the apocryphal book, Peter and Simon Magus, in service of the emperor Nero, engage in a magic contest. A demon comes to the aid of Magus, enabling him to fly. Peter performs the sign of the cross; Magus crashes, breaking his legs “in three parts” (presumably, this is symbolic of the godhead: father, son, and Holy Ghost). The crowd who had gathered to watch the contest turns on Magus, stoning him. Grievously injured, Magus later dies under the knife of two physicians.
The punishment for the Simonists is horrific. They are buried upside down in baptismal basins; their protruding feet are burned by flames. These sinners simultaneously suffocate and burn. The basins in which the Simonists suffocate remind Dante of a baptismal basin which he accidentally broke in Saint John’s Cathedral in order to save someone who was drowning in it. He describes the eternal horror:

“I saw upon the sides and on the bottom
The livid stone with perforations filled,
All of one size, and every one was round.
To me less ample seemed they not, nor greater
Than those that in my beautiful Saint John
Are fashioned for the place of the baptisers,
And one of which, not many years ago,
I broke for some one, who was drowning in it;
Be this a seal all men to undeceive.
Out of the mouth of each one there protruded
The feet of a transgressor, and the legs
Up to the calf, the rest within remained.
In all of them the soles were both on fire;
Wherefore the joints so violently quivered,
They would have snapped asunder withes and bands.”

Dante looks around at the kicking feet and sees one set whose soles are tormented more viciously than others around him. He asks Virgil:

"Master, who is that one who writhes himself,
More than his other comrades quivering,"
I said, "and whom a redder flame is sucking?"

Virgil replies that when they get closer, Dante will see who it is:

"If thou wilt have me bear thee
Down there along that bank which lowest lies,
From him thou'lt know his errors and himself."

Standing before the kicking feet, Dante asks:

"Whoe'er thou art, that standest upside down,
O doleful soul, implanted like a stake,"
To say began I, "if thou canst, speak out."

This is Pope Nicholas III, who had once been the leader of the Inquisition in 1262. Before being appointed to the papacy 1277, when the then-Giovanni Gaetano took the name Nicholas III. This pope was infamous for his nepotism, appointing favored family members to key posts.
Unable to see, the sinner assumes that Dante is Pope Boniface VIII, for whose arrival in Hell the shade has long anticipated. As Virgil instructs him to do, Dante says he is not Boniface.
Irritated, the shade asks what the travelers are doing in Hell. He also tries to excuse his own life of sin, claiming the money he charged was to support his family.

"Then what wantest thou of me?
If who I am thou carest so much to know,
That thou on that account hast crossed the bank,
Know that I vested was with the great mantle;
And truly was I son of the She-bear,
So eager to advance the cubs, that wealth
Above, and here myself, I pocketed.”

The former pope then describes to Dante and Virgil the punishment in Hell for the Simonists:

“Beneath my head the others are dragged down
Who have preceded me in simony,
Flattened along the fissure of the rock.”

They are buried in rock, and their bodies for the entire third “pouch” of the Eighth Circle of Hell. Nicholas says that he will descend lower into the layers of rock when Boniface finally is sentenced to eternal torment as will another corrupt member of the clergy, Pope Clement V:

“Below there I shall likewise fall, whenever
That one shall come who I believed thou wast,
What time the sudden question I proposed.
But longer I my feet already toast,
And here have been in this way upside down,
Than he will planted stay with reddened feet;
For after him shall come of fouler deed
From tow'rds the west a Pastor without law,
Such as befits to cover him and me.”

Boniface’s was Dante’s bitter enemy. This pope vastly expanded the power of the Church. Eventually, Boniface sent Dante, and and many other leaders of the white Guelphs, into exile. Pope Clement V’s sins include moving the Papal See to Avignon, France, from Rome:

“For after him shall come of fouler deed
From tow'rds the west a Pastor without law,
Such as befits to cover him and me.
New Jason will he be, of whom we read
In Maccabees; and as his king was pliant,
So he who governs France shall be to this one."

Tired of listening to Nicholas rants and defenses of his own simony, Dante interrupts the sinner’s diatribe to ask him if Christ would have charged Saint Peter for the keys to the Kingdom of Heaven, or if the Apostle Peter would have asked Matthias for a fee when he replaced Judas, the betrayer of Christ:

"I pray thee tell me now how great a treasure
Our Lord demanded of Saint Peter first,
Before he put the keys into his keeping?
Truly he nothing asked but 'Follow me.'
Nor Peter nor the rest asked of Matthias
Silver or gold, when he by lot was chosen
Unto the place the guilty soul had lost.”

No longer interested in engaging the shade, Dante tells the former pope that he deserves his fate. Before he takes his leave, the poet rails further on the evils of the papacy. He colorfully calls Rome a whore who accepts money from kings for sexual favors. In doing so, Dante argues, the Church is also guilty of idolatry. The Church, therefore, is as culpable as the heretics which they freely condemn:

“Because your avarice afflicts the world,
Trampling the good and lifting the depraved.
The Evangelist you Pastors had in mind,
When she who sitteth upon many waters
To fornicate with kings by him was seen;
The same who with the seven heads was born,
And power and strength from the ten horns received,
So long as virtue to her spouse was pleasing.
Ye have made yourselves a god of gold and silver;
And from the idolater how differ ye,
Save that he one, and ye a hundred worship?”

Not yet finished, Dante goes on to condemn Constantine, the first Christian Emperor (299-337 C.E.) Constantine’s sin, known as the “Donation of Constantine,” was the granting political control of Italy to the Church. In Dante’s estimation, this transfer of power made the Church too wealthy, leading to corruption:

“Ah, Constantine! of how much ill was mother,
Not thy conversion, but that marriage dower
Which the first wealthy Father took from thee!"

Pope Nicholas, who is still listening, kicks his feet furiously. Virgil, attending to his protege's words quietly, is obviously pleased with his charge’s outbursts:

“And while I sang to him such notes as these,
Either that anger or that conscience stung him,
He struggled violently with both his feet.
I think in sooth that it my Leader pleased,
With such contented lip he listened ever
Unto the sound of the true words expressed.”

Virgil then lifts Dante into his arms and carries him over the bridge, and into the last “pouch” of the Eighth Circle. Once on the other side, Virgil puts Dante down and the two step very carefully down into the incredibly steep valley.