All or most of the "powerful" countries being involved, usually directly. Basically take a look at the top military powers, if majority are active boots on ground, running military strategies, fighting and taking a wartime position domestically, you've got a world war.
Really though it's a new-ish term, and highly subjective. WW1 was the Great War until it popped off again. For a modern thought experiment - could the war on terror be considered a world war? Much of the world's fighting power was dragged into it to some degree, but most people would say no.
Long story short, it's a 'world war' when historians decide it was.