Like Penny says, it's the distance between the bed and arm. Most Antique machines have the arm much closer to the bed, and "high arm" became a selling point when manufacturers started making them that way.
My collection is a bit later and other than one or two, I stick to the era of High Arm machines- which is basically what modern machines look like. My collection is mostly 1890-1930 era.
This is my Singer 12, notice how little distance is between the arm and bed -