An internal conflict is the type of conflict that takes place within a character. It refers to the character's thought process, or the decisions the character must make. An internal conflict is also spurred on by a motive and the resolution is central to the plot. In contrast, external conflict takes place between characters. It is usually a "fight, argument, disagreement, or simply opposition" between two characters or two opposing sides (Least Tern, "Literary Terms for English"). Below is an example of both types of conflict.
One example of an internal conflict we see in A Midsummer Night's Dream is Hermia's internal conflict. At the beginning of the story, Hermia is faced with the decision of saving herself from punishment by marrying Demetrius, as her father is commanding, or risking punishment by continuing to refuse, even daring to marry Lysander against her father's will. We see a glimmer of the resolution of this internal conflict when, in the opening scene, Lysander persuades Hermia to leave Athens with him so that they can be married in a neighboring aunt's home, thereby escaping the harsh Athenian laws, as we see in his lines:
There, gentle Hermia, may I marry thee;
And to that place the sharp Athenian law
Cannot pursue us. (I.i.162-165)
Hermia's defiance of her father can also be seen as external conflict. Hermia's father, Egeus, wants her to marry Demetrius and is threatening her with death if she continues to refuse, but Hermia opposes this idea. As Hermia states, she does not want to "choose love by another's eyes" (I.i.142). Instead, she wishes to marry the man she actually loves, Lysander. Since Hermia and Egeus both have opposing perspectives on what Hermia should do, we can see that their argument is a perfect example of external conflict.