In the late 1800's, China, as today, was a big market for trade and everybody wanted a piece of the action. The European nations, the United States, and Japan all wanted to make money there, but the United States had a problem: it was late to the party in terms of influence in the Far East. The Japanese and Europeans (mostly the British, but many others were involved) had essentially divided China up into "zones" in which they were in charge when it came to trade. The Chinese government at the time, too weak to oppose this system, lost out. American businesses were worried that they would eventually be excluded from trading with China all-together.
The United States had been slow to become interested in asserting itself in that part of the world, but taking control of the Philippines seems to have revived interest. Unfortunately, by the time we got there, all the good spots were already taken (so to speak.) Japan and various European countries already dominated China and American interests were suffering. Only two options were available: fight about it, or complain about it. We chose the later.
The Open Door policy for China was an attempt to level the playing field. The Open Door Notes, mainly authored by William Rockhill, essentially proposed the trade within China be opened up to all comers on an equal basis. No longer would nations be able to monopolize chunks of China in order to hoard profit through coercion. Free trade would decide what the Chinese were interested in buying, and while all nations would have access to Chinese markets none would control them.
This policy worked, to a degree. The nations invovled agreed, in principle, but himmed-and-hawed about actually implementing the ideas. In fact, despite what the policies agreed to said on paper, Europeans still tussled for substantial influence at the expense of the others.