Lower labor cost is one of the factors why China is an industrial leader, but it is not sole factor. It is stereotype that they all work for few dollars and rice - they have better overall wages than many other countries in Asia and Africa. Some comparisons show that wages are often better than in Russia, for example, although it is varying by industry. Chinese labor really cheap in agriculture, but in high-tech it is not that low. Industrial sphere is also not that highly dependent on labor cost - wages aren't largest part of price for many products.
One of biggest reasons why China is good for production is development of industry and better organization at all. There are plenty of companies that will do everything you require, and do this fast and reasonably good. Like when you need to get some electronic device, you just do some quick contracts and in few months everything is assembled an running, because there already a large amount of companies who do mass production and can easily fulfill your request. It is very easy to assemble chain of production from scratch (from your point of view), just order what you need and it will be ready.
Compared to this, production in other countries, including developed western ones, may be harder - sometimes there is need for big investments, and seeking proper contractors may be hard, especially if there is almost no one in your country (like for semiconductors). So company that need to put some product into market may get it after few months from China or after few years from some EU country, spending much money in process. Flexible mass production is very efficient when it works on full speed.
Of course this isn't a miracle - China just has large and established industry, they worked hard for years to achieve it, using government sponsorship, tech steal and many other methods. International companies also helped this much by moving production there. First they moved cheap ones for labor, then it slowly become more efficient to move everything, because it is easier to have everything in one place (from management to control). This is started as licensed productions that was controlled from outside, but now situation is different - China started to do innovation, and now it isn't some Bosch/Siemens/Philips who invent something and just produce it in China, but same company that orders complete product from China, and Chinese do everything. Look at electronics, now half of biggest companies that do design are local Chinese, it isn't outsourcing. And transferring production slowly reduces competence of original company, so soon they couldn't do anything without China at all (we already see this).
This still doesn't work economically when product is so specific so China doesn't have developed industry for it, but amount of these products are small, and China is big. Quality also isn't that good (even when company who does outsource says otherwise), but market doesn't work like it is written in books - people would buy product with worse quality just because it is cheaper, money matters more, that's psychological thing but this if offtopic.
There also specific economical, politica and cultural reasons that doesn't allow other countries to easily become second China, while they sit in same position like China in 80s, but this is also very big topic for discussion.