Mousey is correct in suggesting that part of the purpose of the Induction in The Taming of the Shrew is to set a humorous tone. There is a bit more that can be found in the Induction, however, if we look a little closer.
First, as suggested, there really is no "reason" that the Lord decides to convince the drunken Christopher Sly that he is a Lord. The Lord says simply, "Sirs, I will practise on this drunken man," after nearly tripping over Sly, who is passed out from drink on the floor of an alehouse. This decision is a set-up for the comedy that ensues when Sly awakes, and after some convincing decides,
I am a lord indeed,
And not a tinker nor Christophero Sly.
He has convinced himself so well that he switches from speaking in prose (a sign of a low-born character) to verse (the language of the nobility in Shakespeare's plays)!
But the Induction does also serve a purpose beyond the humor it provides when considering the theme of identity in Shrew. In the main body of the play, Kate is "tamed" once she accepts Petruchio's point of view over her own. This happens in Act Four when she finally agrees:
And be it moon, sun, or what you please,
And if you please to call it a rush-candle,
Henceforth I vow it shall be so for me.
This acceptance of another's view of circumstances is foreshadowed by the comic Sly accepting the word of the Lord and the others around him that he is, in fact, a Lord himself. Once he accepts it, he begins to act and behave as if it were true. The same can be said for Kate. Once she accepts that Petruchio is her Lord and husband, she begins to behave in a "tame" obedient way.
There was no real purpose in the induction other then setting a humorous tone before a non-humorous story. Most of the inductions written in Shakespears time were a framework for the story, like book ends. But in this play it is incomplete. The only time Sly is mentioned is the induction and at the end of Act 1 scene 1. After this he is never talked about again, and forgoten.