There were two Greek wars and one Roman war which were distinguished by the name "Social War". What did the word mean in that time period, and what about these wars led them to be called this?
The Italian Social War is called thus because it was, in essence, a conflict between Rome and its 'socii', or allies. One of the meanings of latin socius is ally, or confederate. By the time of the Social War, Rome's control over Italy was over a complex system of bilateral alliances and colonies of varying legal status, and those allies were called socii. Since, in essence, the Roman socii fought more or less united against Rome, this was called bellum sociale, sometimes also bellum Marsicum, because the people of the Marsi were one of the leading opposing powers. And this is why it is called the 'social war', a war between 'socii' or 'associates', if you will.
It is for the same principle that the war between Athens and the 2nd Attic Sea Confederacy and the war between the Aitolian and the Achaean League or Aitolian War are called Social wars.