What is an example of vigorous exercise?

Vigorous exercise should make you breathe rapidly and feel like you are just at the point where you are pushing your body's boundaries, but without doing yourself any harm. Examples include running, cycling, and resistance training.

Vigorous activity is relative to your present state of conditioning.

For example, I am 45 years old at the time of my responding to this question.  However, my profession requires that I run, jump and perform many physical actions.  A similar woman my age who has a sit-down profession may not spend as much time as I do engaging in physical activity.  If we both ride a bike at a vigorous intensity who would be pedalling faster and harder?  Does it mean she is not working vigorously?

Vigorous activity is generally determined using a scale called the RPE Scale.  (rate of perceived exertion).  The American College of Sports Medicine defines vigorous as a 7-8 on an RPE Scale of 10.

Hence, vigorous activity is any activity that you engage where you perceive that you are working at a 7 or a 8 on the RPE scale.

I hope this is helpful to you.

Vigorous Exercise
Activities > METS or A substantial cardiorespiratory challenge sustainable for 20-30 min or > 60% Vo2 Max/HRR

Moderate Exercise
This intensity is defined as any activity that is between 3-6METS or an exercise that is equivalent to brisk walking at 3-4 mph or an exercuse that can comfortably sustained for 45 min or a range of 40-60% Vo2 Max/HRR