Recently, the word "ladylike" has come up in the news. Oxforddictionaries.com defines the word as “appropriate for or typical of a well-bred, decorous woman or girl.” Merriam-Webster.com gives similar first and second definitions, but has a third definition of “feeling or showing too much concern [my own emphasis] about elegance or propriety.”
Going a bit further back, the Online Etymology Dictionary says the roots of the word “lady” are “hlaf” (bread) and "dige" (maid), i.e. “one who kneads bread,” which I think is somewhat ironic (in the modern, colloquial sense) if you compare it to the traditional gender assigned to the word “breadwinner.” It goes on to say that ladylike was used starting around the 1580s to signify a woman whose behavior was suitable for high rank.
However, I’m also thinking about actual noblewomen. One of the most famous Ladies in history was Lady Godiva, a real person. The legend about her riding naked through Coventry to persuade her husband to cut taxes on the townspeople is unconfirmed, but it certainly says something about the mores of the time. What she allegedly did was shocking, but it was done out of charity, and the legend certainly does not condemn her behavior.
Another very different Lady was Lady Nancy Astor. She was a native Virginian, but her combination of saucy wit and pious behavior won her an Englishman (another ex-American, who later inherited a title from his ennobled father) for a second husband. After Waldorf Astor moved to the House of Lords, Lady Astor won his seat in the House of Commons. Her sharp tongue angered many people and amused many others. Some aspects of her character were quite disturbing, but she certainly mattered.
Is being ladylike important? Certainly, courtesy makes it easier and more pleasant to socialize and to work together, but that doesn’t mean that being nice is always the right thing. Sometimes a bit of stridency, or acting in an unconventional way, is the best or even the only way to get anything accomplished. Using strong words and contradicting other people can be ladylike if that's what's needed. Even among ladies, there are many models to choose for one’s own behavior; so if you want to be ladylike, remember that you have power and responsibility, not just to be, but to do.