What is a benefit of multicellular organisms having some specialized cells?

Complex organisms often have specialized cells that carry out different functions. Let's think about this in terms of humans.

One advantage is that this allows the organism to grow bigger. In larger organisms, it is difficult to transport nutrients and waste to and from all the cells of the body. Having specializing cells and systems (in this case, our circulatory system) allows for these processes to occur. You would also then need specialized cells to gather these nutrients and excrete waste (digestive system, respiratory system). Together, these systems and specialized cells make the organism more efficient at carrying out biological processes than if all the cells did the same thing. 

You can also think about this like a society with people who specialize in different things. There are people who produce crops and food, others who build houses and other buildings for people to live and work in, governments for regulating the society, etc. These people all contribute and make the whole system more efficient than if everyone had to do everything for themselves.