She was the first black /female/ senator of either party. But as Perspicacity pointed out, the main point of his meme, she was the first black /democrat/ senator, /period/.
From wikipedia:
"Carol Elizabeth Moseley Braun, also sometimes Moseley-Braun[1] (born August 16, 1947), is an American diplomat, politician, and lawyer who represented Illinois in the United States Senate from 1993 to 1999. She was the first female African-American Senator, the first African-American U.S. Senator for the Democratic Party, the first woman to defeat an incumbent U.S. Senator in an election, and the first female Senator from Illinois."
So yeah, dems get an extra point for her being female. Doesn't quite balance the score when it took them /123 years/ longer than republicans to have /any/ black senators, LONG after the so-called switch, not to mention long after the civil rights act was passed.