I once heard that basic definition of cardiovascular exercise is "exercise that increase heartbeat for a specific amount of time"
Is this true? If yes, can I choose any exercise(like toe touching,leg lifting,etc) for weight loss?
Cardio exercise is any exercise that raises your heart rate. Face it our bodies were made to move. And we all know that to keep our muscles in shape we need move them. This movement makes them stronger and stronger muscles make for a more efficient and healthy body. Your heart is a muscle. Therefore working it makes it stronger. A stronger cardio-vascular system means more capillaries delivering more oxygen to cells in your muscles. This enables your cells to burn more fat during both exercise and inactivity.
You are doing cardiovascular workouts to improve the transportation of oxygen in your body.
When you say a person is in a poor shape, that is he or she becomes breathless just after short time of light physical activities, you actually mean he or she has a poor oxygen transportation.
The way you do such workouts is usually by working as hard as possible in the aerobic area to maximize your need for oxygen.
You can have a good individual indication of the level of oxygen transportation by measuring the heart rate (HR). Note that you cannot compare the HR of two persons and conclude that the one works harder or has a better oxygen transportation than the other one. If you measure the HR of yourself during a single workout (but not during e.g. a year) it is common to assume that the maximal transportation of oxygen take place when your measure the fastest HR.
While it use to be optimal to do exercises with many fast repetitions, you can do literally any exercise you want for cardiovascular workouts. It is just extremely hard to work as hard as maximal oxygen transportation / HR takes place by doing a plank compared to running fast or jumping.
That fact leads to a reasonable definition of cardiovascular exercises: Exercises, which makes it easy to push your body to work in such a way, that maximal oxygen transportation takes place.
Technically speaking, any activity that increases your cardiac and vascular levels by activity is indeed cardiovascular exercise. Whether it's walking, climbing stairs, boxing, or yoga, maintaining your heart rate at a higher level during activity. There are a couple of catches, though.
First, heart rate is a symptom of the activity, not the activity itself. You can't improve your cardio by drinking a lot of coffee. I mention that in part because you mention toe-touching. Toe-touches, like any stretch, can be good cardio-vascular activity, but you're also inverting yourself, which messes with your blood pressure a bit, which may induce a higher heart rate for a time that has nothing to do with the exercise.
Secondly, to simplify things a bit, you're looking to reach an elevated heart rate for a sustained period. Doing a minute or so of fast walking will get your heart rate up and it will stay up for a bit, but your body will quickly catch on that it was only a short burst of activity and it won't give you as many benefits. The trick to good cardio exercise involves getting your body into a state where it's convinced that it needs to keep the engine idling, so to speak, just in case you need to start sprinting to escape the ravening wolves again.
Lastly, not all exercises are created equally. Some will more efficiently exercise your system and, in general, it's best to do movements that apply to what you plan to do. There was a nice quote I ran into at one point about elliptical machines that pointed out that they do a good job of building up cardio, but the odd movement means that all you're really training your body to do is to more efficiently work the elliptical machine. Most people are better off running, or climbing stairs, because that's what they'll actually be doing in their life.