Internal conflicts are those that take place within the mind of a person, while external conflicts take place between a person or group and another entity of some kind. Internal conflicts often have to do with resolving a moral dilemma or making a decision. External conflicts often deal with obstacles that people face in completing accomplishments or in lengthier battles over situational outcomes.
In S.E. Hinton's novel "The Outsiders," one of the internal conflicts that the main character, Ponyboy, faces involves his relationship with his brother Darry. Their parents have died, leaving Darry in charge of keeping the family together. Darry gave up a football scholarship to college in order to stay at home and watch over his two younger brothers, and Ponyboy is frustrated about having his brother treat him like a child rather than an equal. This leads to an external conflict between the two, but Ponyboy has to decide on his own how he wants to relate to his brother.
External conflicts come in several different kinds: person vs. person, person vs. society and person vs. nature. In "The Outsiders," Ponyboy feels like the rich side of town is all against him because of the way the rich boys drive around, start fights and never get in trouble. He feels like that wing of society is bent on keeping him poor and miserable forever.