The White Army (AKA the White Guard, the White Guardsmen, or simply the "Whites") was the armed forces of The White Movement which opposed the Bolsheviks during the Russian Civil War (not to be confused with the October Revolution).

I feel the first half of the first half of the Wikipedia article on the Czechoslovak Legion does a good job giving them context:

The Czechoslovak Legion (Czech: Československé legie; Slovak: Československé légie) were volunteer armed forces consisting predominantly of Czechs and Slovaks[1] fighting on the side of the Entente powers during World War I and the White Army during the Russian Civil War until November 1919. Their goal was to win the support of the Allied Powers for the independence of the Lands of the Bohemian Crown from the Austrian Empire, and of Upper Hungary from the Kingdom of Hungary, which were then part of the Austro-Hungarian Empire.

In my brief research, I'm not seeing anything to indicate that the Czechoslovak Legion did substantially more than other elements of the White Movement (though that's obv the implication of the meme)