The taming of the shrew portrays an English society in the late 16th century that was very patriarchal and male dominated, and because of this women had a submissive role in society.
Society had a very traditional view that men should dominate women and that women should submit to male authority. Therefore men valued & expected women to be beautiful, submissive & obedient. A woman would be seen as 'shrewish' if she was rebellious & behaved badly. In the play Kate is seen to be 'shrewish' and when Patruchio marries her, he tries to mould her into a desirable wife. Petruchio clearly lays out his intentions when he says- "I am he am born to tame you Kate, and bring you from a wild Kate to a Kate conformable as other household Kates." From this we can see that a woman who was not obedient was not considered normal and would have to be 'tamed'.
Kate only realises towards the end of the play that her fighting & hostility against the 'natural order' was useless, and that the societal role of women meant that they had to submissive, compliant and obey male authority. Her character seems to have changed when she instructs the other women that- "Thy husband is thy lord, thy life, thy keeper, thy head, thy sovereign; one that cares for thee," and then goes on to say that love and obedience is "too little payment for so great a debt." It is a complete contrast to her initial behaviour.
Marriage at that time place little importance on love and it was mainly a way to secure money and social status. Because of this women are in a way represented as a commodity, something that can be bought and negotiated with. This representation & attitude is demonstrated when Baptista announces to the suitors that whoever can give the greatest amount of dowry will win Bianca. He says "Tis deeds must win the prize, and he of both that can assure my daughter greatest dower shall h...