How does realism as a concept in international relations apply?
I wonder if you meant to ask us how realism applies in a particular situation. If so, please let us know.
Realism, in general, is a theory of international relations that says that states will always act in ways that are meant to increase their security and promote their national interest. They will do this rather than acting on the basis of morality or religion or ethnic solidarity or any other consideration.
For example, then, we could look at the recent vetoes by China and Russia of a Security Council resolution that would have criticized Syria's actions in repressing its people. China claims to have vetoed that resolution because it is opposed to intervening in the internal affairs of other countries. According to realism, China truly vetoed the resolution because it thought that doing so would be in its own interests. Perhaps China wanted to trade with Syria. Or perhaps China was afraid that allowing the resolution would make it easier for other countries to criticize China with regard to Tibet or Taiwan.
Realism holds, then, that states act in their own best interests and not because of principles like noninterference in the affairs of other states.