In literature, a conflict is a struggle between two opposing forces. Often, these forces represent good and evil. Most of the time, the conflict takes place between the protagonist and the antagonist. However, a conflict can be internal (takes place inside the character's mind) or external (between the protagonist and a force outside of himself).
An example of a conflict is that of Hamlet. In this play, Hamlet has two conflicts. One takes place between Hamlet and Claudius (external), while the other one takes place between Hamlet and his indecisiveness (internal).