Gentleman - A well-mannered and considerate man with high standards of proper behavior.
Lady - exactly the same thing
There's a bunch of other definitions relating to coat of arms and independent wealth and whatnot.
But this is fairly simple, well-mannered, considerate, having high standards of proper behaviour.
Although, this does not really specify as to WHOM those traits need be applied; therefore one must act like this all the time in order to be considered a gentleman/lady. I guess therein lies the challenge.