This speech is given by Biondello, the servant of Lucentio and of Tranio in his current disguise as Lucentio, and is heard by Baptista, Gremio, Tranio (disguised) and Lucentio (as Cambio). It presents a vivid and outrageous picture of the overdue bridegroom Petruchio, on his way to be wed, but clad in the most unlikely costume, adorned with a broken sword, and riding a horse so sorry and broken-down that it seems unlikely the poor beast could bear a rider.
The speech is obviously comic, and is received by most of Biondello's hearers with great amusement. Baptista, the bride's father, is more relieved than amused, as evidenced by his heartfelt:
"I am glad he's come, howsoe'er he comes." III.2.71
Tranio also spares a moment from laughter to offer a possible excuse for Petruchio's wild appearance, suggesting that it is "some odd humour" and that Petruchio is in the habit of wearing clothing not befitting his noble rank. Tranio, of course, has a vested interest in seeing Petruchio accepted as Katherina's bridegroom, since Lucentio's object, Bianca, is not available until her elder sister is wed.
This section reveals all we really need to know about Baptista, the girls' father. So eager is he to see Katherina married and out of his house that he does not balk at the ridiculous and insulting bridegroom who is apparently on the way. Later in the scene he offers some reproofs to Petruchio, but the wedding goes ahead anyway. Baptista's brief moment of sympathy for Katherina—
"I cannot blame thee now to weep
For such an injury would vex a saint" III.2.27-28
is soon forgotten in the relief of Petruchio's arrival.
There is little information to be gleaned about the other characters in the scene (except, perhaps, that Biondello can be wonderfully articulate on occasion), because all have a determination to see Katherina wed, and no-one beyond Baptista has any ties to her that ought to make him reconsider the match in these startling circumstances.
Petruchio's character, however, is to a great extent displayed in this speech. He is a nobleman, and on his first appearance in the play was plainly attired as such. But now, he is entering a 'suppose' of his own, with the aim of taming his shrew. In order to achieve his purpose, he is perfectly able to lay aside the trapping of his rank—as he subsequently remarks,
"To me she's married, not unto my clothes." III.2.116
This is later reflected in the scene at Petruchio's own house in which he scolds and abuses the tailor and refuses to allow Katherina to have the splendid new gown made for her, and insists that they must visit her father
"Even in these honest mean habiliments."
To be sure, his wedding clothes do not reach even this standard, but Petruchio is making a point.
The bizarreness of his heralded appearance also ushers in the worst of Petruchio's wild and contradictory behaviour. In his first meeting with Katherina, he has, it is true, irritated and bewildered her by contradicting what she says, but nonetheless in their first scene together the two of them are very much on equal terms, and if Petruchio manages to get his own way, it is by something very much like cheating. After the marriage, however, his behaviour is so wild and exaggerated that Katherina no longer behaves as his counterpart, but takes the reasonable and proper position, defending the tailor's work, and Petruchio's servants, against his supposed rage. On her wedding day, Katherina will be properly dressed and ready to go to church, only to find that her bridegroom has not bothered to show up on time, and when he does, is not even respectable in appearance.
There is also a connection here to the end of the play, in which the more 'respectable' characters—the ones who use their clothes to disguise their identities—attempt to make mockery of Petruchio. He sets himself up as the butt of the jest by asserting that his wife, whom all know to be a shrew, is conformable and obedient—and then turns the tables on his companions with the truth. In this speech, Petruchio is again setting himself up as the fool, by his absurd clothing (etc), but their laughter cannot worry him because he knows that what is inside the costume is more important. (It appears from the oddness of Tranio's sudden assertions of long-standing friendship with Petruchio, that Hortensio was originally a participant in this scene and that his speeches have been transferred to Tranio. If Hortensio were present, the 'turning the tables' would be more similar to the final scene of the play.)
Stylistically, this section is full of the exuberant language which is used at various points in the play. Gremio's description of his house, in the scene where two suitors are competing to 'buy' Bianca, while quite different in elegance, displays the same virtuoso fluidity with language. It is probable that Shakespeare was quite specifically attempting to outdo the pamphleteer Nash, whose works were in circulation at the time the play was written, and used just such exaggerated and flamboyant language. G R Hibbard describes the language of such passages as "bravura... conscious display(s) of the rhetorical arts of grotesque description, farcical narrative, and inventive vituperation". In fact, Shakespeare is showing off, in a style that may read rather heavily these days, but was written when word-pictures were necessary to paint the scenes for the audience's imagination. The comic description of Petruchio's attire could be confirmed by the character's appearance, but much more attention is paid to his miserable horse, which could not, of course, appear.
And it is not only the audience who must be taught by words how to perceive the action before them. The whole play is concerned with a process of conditioning, in which Katherina—and Christopher Sly—are persuaded by words as much as by actions into a complete transformation. In this passage, the words describe a physical, visible transformation—but elsewhere in the play, words are used to propel the transformation itself—Sly into an honoured Lord, and Kate into someone "sweet as spring-time flowers". II.1.240