The 13th Amendment outlawed slavery
The 14th Amendment stated that no state shall abridge the rights of any citizens
The 15th Amendment, ostensibly, gives the right to vote to African-American men. It states that "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."
So, the 15th Amendment worked to codify, or bring into fruition, a whole new group of voting citizens who had equal protection under the law in a system where slavery is now illegal.