Historically, production in China was cheaper due to lower labor (and land) costs, so over the decades many companies moved labor-intensive manufacturing operations there. In turn, this meant other countries had to start importing these goods from China, resulting in a balance-of-payments deficit. As a result of this China now has a large share of the world's manufacturing base, as well as large foreign currency reserves that can be used to buy goods/land/resources/companies abroad. China has historically used many of these reserves to buy hundreds of billions of dollars worth of US Treasury Bills, so in theory the US is legally indebted to China.
Two things to keep in mind though:
1) China's lower labor costs won't last -- they're rising at 15-25%/year. As a result many companies have already begun shifting manufacturing operations back out of China, this time to even lower-cost manufacturing countries like Vietnam, Malaysia, Burma, etc.
2) China can't really use its US Treasury holdings to bully the US -- in fact, it can't even really count on the value of all the US Treasury Bills it holds. If it starts dumping US Treasuries in bulk, the price of treasuries will drop like a stone and wipe out much of the value of China's foreign reserve. Moreover, US Treasuries are, in the end, just a promise from the US government to pay with no real guarantee -- if China starts using them as a weapon, the US may just opt to repudiate the debt (though not without major consequences in terms of investor confidence and future interest rates).