In King Lear, what does Cordelia mean when she says to her sisters in Act 1 scene 1, "I know what you are"?

Whenever you are trying to focus on what a specific quote
from a text means it is important that you do two things. Firstly, you must consider
what the character says before and after the quote, and secondly you must consider the
meaning of the quote in the light of the context of that scene or chapter as a
whole.

Cordelia therefore says this quote to her sisters
after she has been exiled by her father for not testifying with sufficient eloquence to
the love that she has for Lear. Having heard Goneril and Regan exaggerate and lie in the
hope of gaining more land, Cordelia shows her love with simplicity and not with
insincere hyperbole. As a result, she receives nothing except being cast out of her
father's kingdom. Cordelia, however, clearly sees through her sisters' plot as this
speech suggests:

readability="13">

The jewels of our father, with washed
eyes

Cordelia leaves you. I know you what you
are,

And like a sister am most loath to
call

Your faults as they are
named.

The quote you
identified signifies the way that Cordelia understands the faults of her sisters and the
game that they are playing. However, being too good a character, she will not denounce
them, only leaving saying to them:

readability="8">

Time shall unfold what plighted cunning
hides.

Who covers faults, at last shame them
derides.

Thus the quote you
have identified signifies the animosity that there lies between Cordelia and her sisters
and likewise testifies to the honesty of Cordelia's character.