As New Judge suggests, the word is basically derived from the Latin 'truncus', meaning the main stem of a tree. We also use it to refer to the human body...ie the main torso part minus the head, arms and legs. So, as regards roads, trunk = main as opposed to minor/side highways.
Strangely enough, The Great Trunk Road - possibly the first one so called - between Calcutta and Amritsar, built by the British during the days of the Raj, was probably created using elephants, but its name had nothing to do with them!