It may benefit America in several ways.
1. Outsourcing jobs to other countries increases incomes in those countries, increasing demand for American-made products abroad. Strong East Asian economies might demand American IT services, healthcare innovations, and a variety of other products that America is very good at producing. If other countries remain poor, demand for American exports remains low.
2. Outsourcing increases the competitiveness of American businesses by lowering per-unit costs of production. Company X is probably less likely to go bankrupt if they offshore jobs to Asian countries with lower labor costs, because their products will be cheaper to buy. If I work in marketing, accounting or engineering departments at Company X, I am better off if they offshore the manufacturing, because my job is ultimately safer--since the company is less likely to go out of business.
3. American companies tend to offshore jobs that add lower amounts of value to the product that is being produced. American companies tend to keep jobs at home that add lots of value. When an iPod is built in China, only a tiny portion of the wages go to Chinese factory workers. Most of it flows to American engineers that design the product and American workers that quality test them, do the marketing for Apple, etc. This is true for many products that are actually manufactured in Asia but have their roots in American research, design, engineering, marketing and distribution services.
As a sidenote, be careful not to conflate outsourcing with offshoring. You are presumably asking about offshoring, which is, literally, American companies employing foreign workers. Those workers can be either part of the company (i.e. paid directly by the American company) or they can be employees of an Asian factory (i.e. like Mattel, who just hires a factory and the factory pays the employees). The first case is one of offshoring. The second case is one of offshoring AND outsourcing.
Outsourcing is when companies pay another company to do a job. I worked for an American outsourcing company for awhile, and it was based in America. Major American companies would pay us to handle their customer service--rather than hiring Indian call-center agents, they hired call-center agents in Utah. So you want to ask about offshoring, not outsourcing, it would seem. My answers were geared toward that question.