The system he used meant that he took the same photograph 3 times, once with a red plate, once with a blue plate and once with a yellow plate. When these were put together you got a colour photograph.
He was waaay
ahead of his time then. This was the same 3-color system Technicolor patented and made famous in the movies starting in the 1930s (although Technicolor had developed a 2-color system in the 1920s which was used in the original Ben-Hur). Ironically the Soviet/Russian film studios did all their work in black and white even into Stalin's age mainly because they could not AFFORD color like Hollywood. The Soviets only used color after WWII mainly because they stole the color film process that the Germans had perfected (which had a name which I forget) which unlike Technicolor did not use the three different film/color process but one strip of film. I say stole because the Germans had patented it before the war but the Soviets took the method with them when they took Berlin in the fall of the Nazis, without payment. The German system became Sovcolor in the Soviet Union, Eastman Color in the US, and FujiColor in Japan and is the basis of all motion picture film stock today because it is cheaper to make, to film, to develop than Technicolor (what had to use a giant camera so they could film the same scene with three different strips of film).
Ironically now all these years later it turns out the films using Eastman Color (from Hollywood starting in the 50s) are fading and in need of constant restoration. While the Technicolor three-plate/film process shows little sign of fading (just look at the crispness Wizard of Oz and Gone with the Wind). This could explain partly why Prokudin-Gorskii's pictures with their saturated 3-color style still look so vibrant 100+ years later.
Back to topic - I think we discussed Prokudin-Gorskii's color pictures of the IF of the family in a previous thread. How wonderful it would be if they still exist somewhere.