"It is of course well known that the only source of war is politics ... war is simply a continuation of political intercourse, with the addition of other means." - Carl von Clausewitz, Vom Kriege (On War)
The basic motivation, of course, is willingness to wage war, but motivations may be analysed specifically. Motivations for war may be different for those ordering the war than for those undertaking the war. For a state to prosecute a war it must have the support of its leadership, its military forces, and the population. For example, in the third Punic War, Rome's leaders may have wished to make war with Carthage for the purpose of annihilating a resurgent rival; the army may have wished to make war with Carthage to exploit the great opportunity for plunder while levelling the city of Carthage. But the Roman people may have tolerated the war with Carthage on account of the demonisation of the Carthaginians in popular culture, since there had been rumors of child sacrifice. Since many people are involved, a war may acquire a life of its own -- from the confluences of many different motivations.