Wikipedia says this about the Civil Rights Act of 1964:
"The Civil Rights Act of 1964 (Pub.L. 88-352, 78 Stat. 241, July 2, 1964) was a landmark piece of legislation in the United States that outlawed racial segregation in schools, public places, and employment."
https://en.wikipedia.org/wiki/Civil_Rights_Act_of_1964
The 1968 Act, as star_gazer noted above, had to do with housing. The Wiki says:
"The Civil Rights Act of 1968 prohibited the following forms of discrimination:
"1. Refusal to sell or rent a dwelling to any person because of his race, color, religion or national origin."
What that meant in practical terms in one example personally close to me is that my grandmother, a white Southern racist, had to take down her big "For Rent" sign that advertised the miserable "tenement houses" she rented to whites only. She was not willing to rent to blacks, so from then on relied on word-of-mouth advertising. This was deemed legal since there was no public notice of the availability of that housing. It is perhaps impossible for one who did not live through it to appreciate the sweep of these Acts and the social upheaval they provoked.
It was a "follow-up" in the same sense the 14th and 15th Amendments followed up the 13th.
"The Thirteenth Amendment completed the abolition of slavery, which had begun with the Emancipation Proclamation issued by President Abraham Lincoln in 1863.[4]
The Thirteenth Amendment was followed by the Fourteenth Amendment (civil rights in the states), in 1868, and Fifteenth Amendment (which banned racial restrictions on voting), in 1870."
https://en.wikipedia.org/wiki/Thirteenth_Amendment_to_the_United_States_Constitution
Like some of us at AFT, we don't get everything together on the first try. ;)
More seriously, follow-up legislation sometimes closes gaps, sometimes is the next step in someone's agenda, sometimes puts teeth into text.