This is quite a big question, so I'll try to point you in some thoughtful directions for your essay.
First, you should know that plays in Shakespeare's day were often performed as sort of "command" performances for the nobility. Special occasions as weddings, birthdays, etc. might be celebrated with a performance. Shakespeare's company of actors did not play in the Globe year round, so his plays were also performed in these more intimate circumstances.
The Induction, involving the transformation of Christopher Sly from a lowly tinker to a Lord ends with the arrival of a group of players, meant to perform for this "Lord," and this ushers in the performance of Taming of the Shrew. We can be fairly certain that Shakespeare is making direct reference to the practice I mention above.
This notion, that there is an audience onstage watching a play, while an audience offstage also watches the play is called a play within a play, and a concept favored by Shakespeare because it called the audience's attention to the fact that what is being enacted on stage reflects the audience members' own lives. Think about his famous quote from As You Like It --
All the world's a stage,
And all the men and women merely players.
Shakespeare constantly reminded his audiences that they were watching a performance, but that their own lives too, could be considered in the same way.
The plot of the Induction is thin, but meant to be comic. An actual Lord arrives at an Inn, meets a drunkard (Christopher Sly) and decides to trick him into believing that he is not a drunk tinker but a Lord himself. He does this by having everyone, including a Page (a boy servant) who pretends to be his wife, call him Lord and wait on him with food and drink and a nice bed to sleep in. Christopher Sly settles into this fantasy life without much protest and sits back to enjoy the show performed for his pleasure: The Taming of the Shrew.
A theme to consider about the Induction as it relates to the main plot of The Taming of the Shrew: Kate, like Sly, is convinced to believe, not her own eyes and ears, but the words of Petruchio as to what is real and what is not. In this way, she is "tamed."