Cookies do not usually store sensitive information about you, such as credit card or bank details, photographs or personal information, etc. The data they store are of a technical nature, statistics, personal preferences, personalisation of content, etc.
The web server does not associate you as a person but your web browser. In fact, if you usually browse with the Chrome browser and try browsing the same website with the Firefox browser, you will see that the website does not realise that you are the same person because it is actually associating the information with the browser, not the person.