Conflict is what happens when opposing forces collide. Conflict is the essence of every good story. Without it, nothing happens. The three classical forms of conflict are:
Man vs. Man -- Here the protagonist is struggling against another person, such as in "Free Radicals" by Alice Munro.
Man vs. Himself -- The protagonist struggles against personal demons. A perfect example of this is in the films "A Beautiful Mind" and "Leaving Las Vegas."
Man vs. Nature -- Pick any natural disaster flick to illustrate this one: "Dante's Peak," or "Twister." The characters struggle against a force of nature.
After the classics, there are other examples of conflict:
Man vs. Society -- Think To Kill a Mockingbird or the character of Colonel Aureliano Buendia in One Hundred Years of Solitude. This type of conflict could also be considered to be man vs. man (men).
Man vs. the Supernatural -- Depending on your thoughts about the supernatural, this one could fit into other categories (notably man vs. himself and man vs. nature). Something Wicked This Way Comes by Ray Bradbury is a good example.
Conflict is what gives the story drama. It is what keeps readers reading or viewers viewing. Without it, you would most likely be left with something very dull.