The Thirteenth, Fourteenth, and Fifteenth Amendments are often known as the "Civil War Amendments" or the "Reconstruction Amendments" because they were passed in the aftermath of the war and amidst the political ferment of Reconstruction. Each was concerned with protecting the basic rights of African-Americans newly liberated from slavery by the war. The Thirteenth Amendment outlawed slavery permanently, the Fourteenth Amendment extended citizenship and "equal protection" under law to all citizens (a term it also defined), and the Fifteenth Amendment protected, or attempted to protect, the right to vote for African-American men. Even as these amendments were being passed, their provisions--especially the Fourteenth and Fifteenth Amendments--were being challenged by white Southerners, and while there was a window where black men enjoyed their protections, this period quickly waned with the end of Reconstruction and the establishment of Jim Crow.
In the long term, the Fourteenth Amendment in particular has taken on added significance for several reasons. One is that the Supreme Court has used it to overturn unequal laws--most famously in Brown v. Board of Education. The Court has also used its guarantee of equal protection and equal "provisions and immunities" to expand the provisions of many of the other amendments to the states. This basically meant that states, like Congress, cannot pass laws that violate amendments like the First, the Second, the Fourth, and so on. The definition of citizenship in the Fourteenth Amendment has also proven significant in that it formally establishes citizenship by birth, which guarantees citizenship to the children of immigrants. The Fourteenth has thus proven to have the most lasting--and the broadest--significance, though the Fifteenth has also been invoked to overturn discriminatory voting laws.