Section I of the Fifteenth Amendment to the U.S. Constitution, which was formally ratified on February 3, 1870, states the following:

The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any state on account of race, color, or previous condition of servitude.

The defeat of the Confederacy in the Civil War did not resolve once and for all the issue of racial discrimination; on the contrary, the Voting Rights Act of 1965 was passed exactly one century following that war's conclusion, and was drafted as a response to the country's failure to definitively resolve the problem of racial segregation once and for all.  The disgruntlement brought about among many Southerners from their defeat in the war, the physical and economic devastation the South endured during the war, and the humiliations associated with Reconstruction all conspired to aggravate efforts at reforming that vast region. In order to institutionalize the ideals embedded in the Constitution while enforcing Executive edicts regarding the treatment of former slaves across the South, the Fifteenth Amendment was drafted and ratified.  As the above wording indicates, it was intended to ensure full voting rights for blacks, but, as the reference to the 1965 Voting Rights Act notes, its full implementation would take another one hundred years.

The Fifteenth Amendment to the Constitution of the United States is important because it guarantees voting rights to all American males of all races.  

The Fifteenth Amendment is one of the "Civil War Amendments" that was meant to give African Americans equality with white Americans after the end of slavery.  To that end, it said that no one's right to vote could

be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude.

Of course, the intent of this amendment was subverted by Southerners for decades after it passed.  They used various tricks to deny African Americans the right to vote while not explicitly banning them on the basis of their race.  The 15th Amendment finally came to truly have an effect when the Voting Rights Act of 1965 was passed by Congress to enforce the amendment.