means The stub of a tree, limb, or other thing left after the main part has been cut, broken, or worn away — and, by extension, to baffle someone or to travel about making political speeches.

from From Middle English 'stumpe,' with cousins across the Germanic family — Middle Low German 'stump' and Dutch 'stomp,' all carrying the sense of something blunt or cut short. The political meaning is purely American: frontier orators literally stood on tree stumps to be seen and heard while addressing a crowd, so a candidate going 'on the stump' was once doing exactly that. The sense of being 'stumped' — left blocked and baffled — likely grew from settlers whose plows kept jamming against stubborn stumps hidden in newly cleared fields.