The literal meaning of the word 'Kaur' is Prince. It is believed to be a derivative of the word 'Kanwar' meaning Prince, whereas, 'Singh' is derived from the word 'Simha' meaning lion. It is rather interesting to note, that even Male Sikhs in the past have used (and possibly even today use) 'Kaur' in their names. Read more on the Kaur Etymology.
Birendra Kaur, Ph.D. in her paper, Insight and Foresight exemplifies the role of women as bearing great responsibility. "...Today, we women hold our heads high for the contribution of Sikhism. Women of yore in every sphere, be it service, leadership, or sacrifice. Nowhere else does a woman enjoy such a respectable status as in Sikhi. The Guru has lovingly called us 'Kaur', which means a crown prince - i.e., on whom lies great responsibility."
In 1699, Sikh Women were given the last name 'Kaur' and and Men 'Singh' by Guru Gobind Singh, the tenth Guru of the Sikhs. This initiate intended to end the caste system, social stratification and much of the apparatus of Hindu ritual and legalism. In Indian society, an individual's name reveals his or her caste, and Sikhs were freed from the caste system by having all men incorporate Singh in their names and all women, Kaur. Based on the premises of gender equality, Kaur was also given to Sikh Women to establish an identity independent of their father or husband.
Most Sikh first names are gender-neutral. For example, Harpreet could be a male or female's first name. What identifies Harpreet Kaur as a female is the word Kaur following the first name. Naming a new born.
Even though Sikhism is an ideally progressive social structure, ironically, some still find it difficult to let go of the caste system and the use of last names. The use of Family Names is still prevalent and most people tend to use Kaur and Singh as middle names. A recommended action plan is stop using the last names like Aurora, Sodhi etc. Not to reiterate, but if you are still wondering why you should go about changing a name you have become accustomed to?