She is referring to the Duke's jester, Touchstone, who has just entered.

As you know, the reputation of a court jester is that of one who is very sharp of wit (though he may feign ignorance), and their job (at least in their literary representations) is to entertain the court with witty remarks and banter, often at the expense of the courtiers.  It takes a very witty courtier indeed to match wits with a good court jester, and Celia is suggesting, by calling Touchstone 'the whetstone of the wits', that a person can sharpen her own wits, her own skill at verbal parry and thrust, through conversation with the jester.

You already know, I hope, that a whetstone is a tool for sharpening knives, scissors, needles and other sharp implements.  And here, Shakespeare's literary device is the metaphor of Touchstone as whetstone and cutting wit as cutting knife.

(The on-line version to which I referred is indicated below.)

As you mention in your tag, Celia is referring to Touchstone when she talks about the "whetstone of the wits" in this scene.  She is saying that fools like Touchstone are made to help sharpen the wits of "regular" people.

What she means is that the words of fools make us have to think.  Fools were generally people whose job (one of them at least) was to say things that sounded really stupid, but that would make people think.  They were supposed to point out what powerful people were doing wrong.

This means that fools' words made the listeners (hopefully) reevaluate the things they did.  This, you can say, would help them sharpen their wits.