Doing something vigorously means doing it with a lot of physical force and energy — shaking your head vigorously, rubbing a stain vigorously, exercising vigorously. The body is really moving. But it has a second, very common use where no body moves at all: when someone argues, denies, defends or opposes something vigorously, they do it strongly and without backing down. Newspapers love this one — 'the company vigorously denied the report' is almost a fixed phrase. Notice that vigorously is nearly always positive or neutral about the effort, even when the action is a fight; it says 'with real force', not 'angrily' and not 'rudely'. It goes most naturally with verbs of doing (shake, stir, rub, exercise, campaign, deny, defend, oppose), not with verbs of feeling — you do not love someone vigorously.