When Jordan refers to the fundamental piece of Civic right legislation in the century she means that

She meant the Civil Rights Act of 1964

Explanation:

Barbara Jordan refers to the Civil Rights Act of 1964 as the fundamental piece of Civic rights legislation. This legislation was key to stop segregation in the US, which was one of the main problems the country faced in the 1960's. The legislation made illegal any act of discrimination to people on the basis of one's sex, race, national origin or color.