Cuba Libre means "free Cuba", and was named as a toast to the liberation of Cuba from the Spanish. Two things occurred at the turn of the 20th century, the end of Cuba's War of Independence and the arrival of the then new Coco-Cola in Cuba which by 1900 was widely available. A US soldier garrisoned there ordered the drink and proclaimed "Por Cuba libre!"
Rum and Coke, or a Cuba Libre is a highball cocktail. Highball is the name for a family of mixed alcoholic drinks that are composed of an alcoholic base spirit and a larger proportion of a non-alcoholic mixer.