We can summarize this line as a statement on being careful in the social world. Have tact. Be careful. Be cagey. "Don't put all your cards on the table." At least, try to refrain from exposing yourself in full to the knowledge and the whims of others.
In the context of the play, this is advice that King Lear could have used in the beginning. Tragically, it proves, Cordelia is a foil to the folly of King Lear.
Cordelia can be seen as acting on the advice of humbly presenting herself and she suffers for it. When Lear demands that his daughters compete for the largest share of his kingdom by testifying to their love for him, Cordelia speaks without exaggeration.
"[Lear] receives embellished speeches of endearment from the older two, but Cordelia modestly speaks the truth, angering her father who disinherits her and banishes her forever" (eNotes).
Although Cordelia is banished, she maintains her integrity and finds love. She is the best example of a virtuous person and thus retains her human value, where others (including Lear) struggle and often lose their moral qualities.
Lear, having exposed himself to the caprices of his other two daughters finds no sympathy. He has, in essence, given himself away by proffering his kingdom to Goneril and Regan, going against the advice inherent in the line in question.
"Have more than thou showest, speak less than thou knowest, lend less than thou owest."
Unfortunately for Lear, he does not heed his own wisdom as expressed early in the play.
"Allow not nature more than nature needs / Man's life is cheap as beasts'"
By giving away the property of his kingdom, he gives away his power and puts it in the hands of those whose natures are, perhaps, unsuited to such wealth and power and so immediately abuse it. He has overestimated the esteem two of his daughters hold for him and has overestimated the quality of their natures, giving them more than they need.
The result is that Lear is left utterly exposed to the vanity and corruption of Goneril and Regan and ultimately turned away, exposed to the raw powers of nature, alone and mad in the wild.
This is much like the advice that Polonius gives to his son in Hamlet.
"Have more than thou showest" quite simply means don't go throwing your money around and letting everybody know how much money you have. In other words be moderate in how you present yourself to the world.
"Speak less than thou knowest" in other words, listen, don't talk. If you talk to much you might let slip something you don't want people to know or you could "stick your foot in your mouth" so it is better to listen to others and speak only when you have something relavent to say.
"Lend less than thou owest" is almost like "neither a borrower nor a lender be" in the advice. To lend out money, especially to a friend, is really tricky, particularly in trying to get get your money back sometimes so it is better not to lend your money out.
In all the advice is to keep a low profile and not call attention to yourself through your actions or speech. Live in moderation.