The goal should be to get the cardiovascular system "fully opened up" and then keep it there for a good period, like 20-30min or so. As your cardiovascular system gets in better shape, the amount of work it takes to get to this state will increase, but the actual HEARTRATE can actually go down (because you are pumping more blood per beat, carrying more oxygen, etc). This is completely different from interval training (sometimes called HIIT these days). Once you start doing cardio for a while, you can easily tell when there is a heart rate your body wants to work at when your cardiovascular system gets to its optimal level.
The real trick is finding a form of cardio that doesn't limit you by muscles going anaerobic. For example, if you are on a bike, your quads may burn, which can limit you from reaching full a full cardio state, you shouldn't be limited by anything burning. For me, the elliptical does this for me very well. A fully engaged cardiovascular system FEELS really good, kinda like a muscle pump but in your whole body, once you get in good enough shape.
The problem is, most people don't want to work this hard, or put in the work to get in good enough shape so it's really not hard work, they want an easier version of cardio, like LISS or HIIT...