External conflict is referred to as "Man against..." Common conflicts include man against man, man against nature, man against machine and man against the supernatural.
Short stories usually have one central conflict, while novels likely have several. A character may face problems simultaneously or sequentially.
Conflict makes a story more exciting. Done properly, it holds the reader's interest, adds tension, propels action and gives a character purpose.
External conflict involves a character searching for a way to solve the problem, then acting on it. These actions should intensify the story, and possibly lead to more conflict.
Conflict is resolved during the story's climax, in which the character either overcomes the problem or succumbs to it.
External and internal conflicts can be combined in the same story when outside forces create moral dilemmas for the hero.