Devil May Cry 3 starts with Dante's yet-unnamed shop in the early 1990s. A mysterious man, Arkham, arrives with an invitation from Dante's brother Vergil in the form of a demonic attack. After Dante defeats a group of demons, a huge tower erupts from the ground nearby, eclipsing the sprawling city of Angels (Los Angeles) surrounding it. Sensing that Vergil is on top of the structure, Dante interprets this as a challenge. He begins fighting more demons during his journey, some of which become his weapons once defeated. Dante is attacked by a woman on a motorcycle who turns out to be Mary, Arkham's daughter, who wants revenge on her father for causing her mother's death. It is revealed that Arkham works for Vergil; they plan to take Dante's half of their mother's amulet and use its power on the tower to connect the human and demonic worlds.
The gameplay in Devil May Cry 3 consists of levels, missions, in which players battle enemies, carry out platforming tasks and solve puzzles to progress through the story. The player's performance in each mission is graded from D through C, B and A, with top marks of S and SS. Grades are based on time taken to complete a mission, the number of red orbs (currency obtained from defeated enemies) gathered, "stylish" combat, item usage and damage received. The games tracks stylish combat by an on-screen gauge, which is the performance of a series of attacks ("combos") while avoiding damage. The longer a player attacks without repetition and evades damage, the higher the score.
Source: Wikipedia, "Devil_May_Cry_3:_Dante's_Awakening," available under the CC-BY-SA License.