It means that everyone is equal, we all have the freedom of life liberty and pursuit of happiness, and that to make sure we have these and our rights are not impeded upon, we have created and managed our government, and our government gets its power from the citizens of the USA
The term that is defined as “a legal doctrine that permitted racial segregation in public facilities" would be "Jim Crow", which was a series of such laws passed in the South after the Civil War.
