Actually it is not that important to the Devil May Cry series. It's just a game with a title "Devil May Cry 2" and thus we fans want it, and it
is good as a game but not as the usual Devil May Cry game.
Anyway the story without spoilers.
Dante is invited by another Devil Hunter, Lucia, to help gather some mysterious artifact that will help defeat the current bad guy.
There are two cds. One with Dante and one with Lucia. There are more or less the same missions with slight differences.
Hope I explained that right.