Mental stabilization, or concentration, is a mind whose nature is to be single-pointedly placed on a virtuous object and whose function is to prevent distraction. Concentration is a transversal stage of the path, meaning we practice it with respect to all of the other stages of the path. We train in concentration with respect to each of the other stages of the path, taking each object deeper and deeper within our mind. We begin by simply holding our mind single-pointedly for a few seconds, and we keep training in concentration until we attain tranquil abiding. With tranquil abiding we can remain single-pointedly placed in concentration on our objects of Dharma forever if we wish. The mind of tranquil abiding, though, is not the end of our training in concentration. It is merely the first level of concentration of a desire realm god. Our body may be that of a human being, but our mind is that of a form realm god. We continue to train in all the different absorbtions of the bodhisattva’s grounds and paths, taking our mind higher and higher until it reaches the peak of samsara. But even that is not far enough, since that realizes our objects of Dharma merely with our gross mind. To attain enlightenment, we must learn how to bring the objects of Dharma into our subtle and very subtle minds. We can only do this through training in Tantra. Tantra teaches us how to make manifest our subtle and very subtle minds so that we can learn to meditate with them. Eventually, we need to directly realize each and every one of the stages of the path with our very subtle mind of great bliss. Fortunately, however, once we realize one object with any given level of concentration, it is not that difficult to realize all of the other objects with the same level of concentration, much like with the strength to lift a 100 pound box also enables us to lift a 100 pound chair. Also, there are certain objects of meditation, like bodhichitta, emptiness, generation stage and completion stage, which are actually the synthesis of all of the previous objects of meditation, so by realizing these special objects directly we realize all of other objects indirectly.
The actual training in concentration begins with “seeking, finding, holding and remaining.” First we seek our objects of meditation through analytical meditation until we first find them. We then hold them for longer and longer periods of time until we can remain with our object throughout the entire meditation session without ever losing it. When we train in concentration, we abandon gross and subtle mental excitement and sinking. Gross excitement is when we lose our object of meditation completely for an object of attachment. Subtle mental excitement is when part of our mind is with the object but part of our mind is with another object. Gross mental sinking is when our mind becomes so dull that we lose the object completely and we are practically alseep. Subtle mental sinking is when the focus of our objects wavers somewhat, but we haven’t lost it.
The perfection of concentration is training in concentration motivated by bodhichitta. To understand this, we need to realize the relationship between concentration and attaining enlightenment. Concentration functions to mix our mind with its object. According to the Prasangika teachings on emptiness, mind and its object arise in mutual dependence upon one another – there is no object without a mind and without an object there is no mind. In reality, we can say that the mind and its object are actually two aspects of the same entity. Once again, the analogy of Play Dough proves useful. The mind is the Play Dough and the object is essentially the aspect or shape that the Play Dough takes. When we concentrate on any given object of Dharma, we are for all practical purposes holding our mind in the shape or aspect of our object of Dharma. When we concentrate on virtuous objects, it functions to render our mind peaceful and controlled. It is explained in many texts that the principal cause of happiness is mental peace. When our mind is peaceful, we are happy; when our mind is unpeaceful, we are unhappy. Concentration on virtue renders our mind peaceful, and therefore happy. The greater the concentration, the greater the inner peace. It not only does so for the moments we are happy, but each moment of concentration functions to create a seed for the experience of future happiness. The longer the duration and the deeper the intensity of our concentration, the longer the duration and the deeper the intensity will be the resulting seed. We can think of it like attaching a balloon to a helium machine. The longer you keep it connected, the more inflated the balloon becomes, and the higher the pressure of the gas the faster and more intensely it fills. The difference is our mind is an infinitely elastic balloon that has no limit to how far it can be inflated with virtue. To illustrate the power of concentration, it is said that just one moment of concentration on love with a mind of tranquil abiding is enough to create the cause for an entire lifetime as a long-life god.
Emptiness greatly increases the effectiveness of our concentration. We normally grasp at inherently existent objects of Dharma, inherently existent meditating minds and inherently existent meditaters. If an object of Dharma is inherently existent, then it is actually impossible for a mind to concentrate on it because the object of Dharma is separate from the mind. If a mind is inherently existent, it cannot mix with any object because doing so would change it and inherently existent things are unchangeable. And if the meditater is inherently existent then they could never benefit from their mind meditating on objects of virtue because there would be no connection between the meditater and their mind. But when we realize the emptiness of these three, it becomes very easy for our mind, its object and ourselves the meditater to all mix together like water mixes with water. It was discussed above how mind and its object are like two aspects of the same entity. We also naturally impute our I onto our mind. So if the only object of our mind is the object of our meditation (meaning we have perfect concentration) and we naturally impute our I onto our mind (which in this case is the subject/object union) then we literally become our object of meditation. The meditater, his object and his mind are three different aspects of the same entity. This reveals an extremely powerful effect of concentration combined with an understanding of emptiness: we become that which we concentrate on. If we concentrate on love, we become a loving person; if we concentrate on compassion, we become a compassionate person; if we concentrate on the deity in our Highest Yoga Tantra practice, we become the deity. If we understand this clearly, we will find it effortless to generate the desire to train in concentration.
Kadampa Working Dad 
Thank you again Kadampa Ryan!