A blue plastic tarp may be the first thing that someone visualizes when they hear the word "tarp," but if you put the word in a more historical context, they will tend to instead visualize canvas tarps. This is fairly easy to understand, as poly tarps were introduced to the market as recently as the 1960s! Prior to this innovation, all tarps were made of canvas.
"Tarp" is an abbreviated form of "tarpaulin," which in turn came from the words "tar" (used to waterproof the material) and "palling" (a heavy cloth covering). These early tarpaulins were the invention of sailors keeping their cargo dry at sea.
There are certainly benefits to using a canvas tarp; they are even preferable in certain situations. However, it's difficult to ignore that the traditional aesthetic plays a big part in the material's popularity. Olive drab canvas tends to evoke vintage military gear and turn of the century outdoor adventures, as the green color was commonplace in those circumstances. Khaki canvas tends to bring to mind desert campaigns, the color blending into sand dunes.
Another aspect of canvas tarps that adds to their allure is the fact that many are made of cotton. Products made of natural fibers are a perennial favorite, especially as people look for alternatives to petroleum-based manufacturing. Cotton is a renewable resource, and when it is discarded someday it will be capable of biodegradation. In many ways, canvas tarps are a greener, more environmentally responsible option.