Internal and external are the two types of conflict that drive a plot forward. Both types of conflict are usually necessary to make a story interesting to readers. Although they are different, internal and external conflict are related.
Internal conflict is a complication that happens within a character; it may be a moral dilemma the character is facing, or it may take the shape of a choice or a desire. As author Kurt Vonnegut said, "Every character should want something, even if it is only a glass of water."
Internal conflict creates individuality for a character; it sets her apart from the rest of the story and gives a motivation for choosing certain actions. It can also be directly related to external conflict.
External conflict occurs between two or more characters, or a character and his environment; external conflict involves an interaction with the setting and other characters of the story. Wars, fights, love affairs, trying to get a taxi and all other situations in which characters clash create external conflict.
External conflict sets the overall tone for many stories. Multiple characters can be motivated by external conflict, and it creates situations in which characters are forced to interact.
Internal and external conflict play off one another. For example, a man struggling with a decision about whether to quit his job may snap at another character, which causes the two of them to fight. In situations like this, internal and external conflict have a direct link.