Yes, Catherine the Great was a real person and was one of the most famous rulers in Russian history. The Great covers the basic facts of her biography pretty accurately. She was born Princess Sophie von Anhalt-Zerbst-Dornburg, a member of a minor German royal family, and was selected to be the wife of the Russian emperor, Peter III. Some of the details in The Great, such as her interest in reading philosophical texts by Enlightenment writers, are also true to life.
The major plot arc of The Great is also accurate. Frustrated with her inept husband's rule, Catherine did, in fact, lead a conspiracy to overthrow Peter, which happened in 1762. Catherine went on to rule Russia as empress until her death from a stroke in 1796. Her rule did implement many of the reforms she longed for (including the first institute of higher learning for women), bringing Russia into a more modern world alongside the rest of Europe, but it wasn't all sunshine and philosophers: her reign also included conflict over serfdom and anti-Jewish policies, among other controversies.