Well, I was hoping to see a few more responses before chiming in... noone's commented.
Could be referring to a few different notions.
"New World Order" is a few different things.
The most common is using this term to describe when the world changes or is altered by a war, political shift in power or something of that nature. It's been used by various people to describe post-wars (WWI, Cold War and WWII) - after which the world political compass shifted. Along this line it has also been used to note when we became a nuclear-world, for example. Using this thought you could apply this to the era in which firearms were invented, altering politics, and the discovery of America and so on so forth - any time a new progression or advancement changed the way countries deal with eachother.
The term itself has been attributed as far back as Alexander the Great, whose ultimate goal was to create a 'new order to the world', his order.
The Conspiracy Theory with this term centers around the idea of a world-wide government or, a multinational government somewhat like the European Union but more complete. The first of these two (the world-wide government) would be akin to Star Trek, actually, in theory.
That's not quite accurate of the 'in depth' 'conspiracy theory'... Look at the Olympic rings, the symbolism of these rings is the 5 continents linked together. There are different 'arms' of the global political structure that are already essentially in place. The UN and the IMF / World Bank are the most known of these 'attempts' at a global governance system. Simply, they haven't been able to garner the support required to have enough member nations surrender their sovereignty to this system.
So, the way it will work will be much like the european unions creation, there's already the treaties signed for the north american union (Canada, US and Mexico), also the creation of an asian, african and south american union. In each of these cases a portion of each member nations sovereignty is surrendered to a higher governemtn with less connection to the individuals. From these various unions and less representation of the people, those in charge of these various unions (like in european union, will be unelected) and they will surrender the sovereignty of each of these unions to the UN (or whatever the name might be changed to)... this will allow the world bank to be the global taxing and currency arm to create a world currency... you'll still have your regional currency kept in tact, but it will be tied to it's value relative to the international monetary unit.
Now, I agree that if we could build a global republic, it would look very much like a 'Star fleet' type of organization... and we as a species can go off into the stars.
Here's the caveat : The majority of the nations around the world are NOT republics, or even democracies. Most countries are controlled by some sort of dictator / tyrant. Now, if you take a room that's full of tyrants and petty dictators, and they are trying to agree on a global governance structure... shake them all up, and it's VERY unlikely that you will wind up with a peace loving humanitarian world government.... ESPECIALLY when the majority of the planning of this world government is being planned in secret.
Think about it, even in the most overt discussions for globalization : The G# meetings is a prime example, where any civilian within a 10block radius of the meeting is hosed down, beaten, pepper sprayed, tear gassed and occassionally killed... MEANWHILE the media gets to cover the 'topics of discussion' and the 'plans', but then gets shut behind another set of closed doors where actual discussions take place.
