From what I can find it was a surname of French revolutionary Jean-Paul Marat. What it means in French, I have no idea. Maybe a French expert can help out.
However, the name Marat (Марат) became common among the Tatar people after the 1917 revolution, when they began to name their children after various European revolutionaries (http://en.wikipedia.org/wiki/Tatar_name, see section 4).
A famous bearer of this name is tennis star Marat Safin. A Soviet Russian sub was also named Marat.