First of all, we have to note that not everyone would say that regional organizations actually do promote globalization. There is a clear argument to be made that such organizations only promote regionalization, not globalization. This argument must be accounted for in this discussion.
We can argue that regional organizations like the European Union or the North American Free Trade Agreement region promote globalization. This is because they encourage countries to look beyond themselves. They break down the barriers between countries and lead to a situation in which countries cooperate with one another and make rules that apply to multiple countries. This can surely be seen as a form of globalization.
However, it is also possible to argue that this hinders globalization. This argument holds that a united Europe, for example, is not more likely to trade with the NAFTA region than it was before. In fact, it can be argued, the EU might prefer not to trade because it will feel that it can be self-sufficient to a greater degree than (for example) Germany would feel it could be. Thus, by this argument, regional organizations lead to a world which is divided up into regions, not a world that is globalized.
Thus, if regional organizations do contribute to globalism, it is because they allow countries to connect with one another and create things like rules that govern more than one country. However, it is possible to argue that regionalization actually slows globalization.