Can anybody help me out on the concept of dharma as it applies to The Ramayana. Dharma of the characters such as: Rama, Sita, Bharata, etc.
Dharma is a complex concept in the Hindu ethos. It can be translated as "righteousness," or "morality," or "law." It has been translated famously as "duty." If you take this constellation of terms as its meaning, then you get a sense that dharma is the right way to act, with integrity, to do what you ought to do.
One way this plays out in the Ramayana is in the sense of duty or loyalty to each other. In the beginning of the Ramayana, a situation is set up in which Dasharatha, king of Ayodhya, must name his son Bharata as his successor, instead of Rama, as he planned. Yet both of these princes are presented as virtuous: they both end up obeying the wishes of their father. Bharata takes the throne and Rama goes into exile.
Lakshman is Rama's brother and Sita is Rama's wife; they both follow him into exile. So there is a sense of acceptance of their fates, and "doing the right thing" involves following Rama into exile.
The idea is that when everyone acts according to dharma, instead of personal desire, then society will be ordered. By contrast, Ravana acts according to his desire, and flies off to kidnap Sita. He is the exemplar of immorality.
One way this gets played out is that people look to Rama and his companions as models for ideal behavior. When he returns to power in Ayodhya, Rama is seen as the ideal king, becuase he always does what seems to be the right thing. Lakshman, Hanuman, and Sita are virtuous because they submit to royal authority and accept their status in life.
(Note that the result of this loyalty is that Sita ends up being banished, and in the end is swallowed by a chasm in the Earth.)