This is a good question. Foreign investment is the money that one country invests in another country. So, if the United States invests in China, then the United states would have foreign investments, because the money is going outside of the country. The host country would be China, because they are getting money from the United States.
The benefit of such an arrangement are several. First, if the investment is a good and wise one, then both countries can benefit. A good investment is profitable for all. Second, since the investment is between two countries, there is the issue of currency difference. So, there is the possibility of making greater money, because one currency can strengthen and another can weaken. So, to use the two countries above as an example, if the Yuan (Chinese currency) gets stronger, then the more of it you own, the money you will make.
The downside of all of this is that investments can be poorly made. At this point everyone loses.