That lord that counsell'd thee
To give away thy land,
Come place him here by me,
Do thou for him stand:
The sweet and bitter fool
Will presently appear;
The one in motley here,
The other found out there.
Dost thou call me fool, boy?
All thy other titles thou hast given away; that
thou wast born with.
This is not altogether fool, my lord.
No, faith, lords and great men will not let me; if
I had a monopoly out, they would have part on't:
and ladies too, they will not let me have all fool
to myself; they'll be snatching. Give me an egg,
nuncle, and I'll give thee two crowns.
What two crowns shall they be?
Why, after I have cut the egg i' the middle, and eat
up the meat, the two crowns of the egg. When thou
clovest thy crown i' the middle, and gavest away
both parts, thou borest thy ass on thy back o'er
the dirt: thou hadst little wit in thy bald crown,
when thou gavest thy golden one away. If I speak
like myself in this, let him be whipped that first
finds it so.
In context, the Fool is chiding Lear for dividing up his kingdom and for giving his titles and his crown away. He invites Lear to call forth the one who counseled him to divide his kingdom; he would show Lear for the fool he is. With Kent's supporting comment, he goes on to name the lords, great men and ladies as fools themselves. To reinforce his point that Lear's actions were those of a fool, he offers him a fool's crown, two halves of a cracked egg, while emphasizing the poor thought that went on in Lear's "bald crown" [head] when he split and gave away his "golden" crown of the monarchy. Here, Lear's two crowns, his "bald crown" and his "golden one" are symbolized by the two crowns of egg halves.
So often in this bleak tragedy Shakespeare uses the Fool to comment ironically on the actions of others in the play under the guise of his status as a fool, which means he can say ridiculous things that if we examine them closely actually criticise the main characters. The Fool performs exactly this role in this quote where he comments on how stupid Lear was to give his land away for nothing and also to people who will not use his gift wisely. It is as stupid as buying an egg for two crowns (far too much money to pay for an egg).
What the fool is doing here is making fun of Lear for giving away his land to his daughters. The fool knows that Lear is making a mistake, thinking that Regan and Goneril will still value him once they have his land and power. So he says, basically, that what Lear has done is as dumb as paying two crowns for an egg.
The fool means that if Lear gives him an egg, the fool can crack the egg in half and give Lear the two halves of the shell as "crowns." The fool explains this meaning right after he makes the remark you quoted. As others have noted, the fool is mocking Lear for having divided his kingdom.
I like #5's explanation! However, I think the most common interpretation will be the one mentioned by others, that the Fool is acting as a conscience for the King, who will accept his criticism in the form of a joke where he would not accept it plainly spoken.