The word "imperialism" describes a process where a nation attempts to expand its influence beyond its own borders by gaining control of territories or peoples. This can come in a number of different guises, most of which were interrelated.
One obvious example of imperialism would be when a nation annexes another territory, as the United States did with the Philippines and Puerto Rico after the Spanish-American War. These territories had belonged to Spain, and the United States, as the victors, formally annexed them rather than allowing them their independence. Another classic example of this form of imperialism would be the control of India by Great Britain from the mid-eighteenth to the twentieth century.
Another form of imperialism would be economic imperialism. This can take many forms, but one of the most blatant historical examples of economic imperialism was the process of carving China up into "spheres" of economic influence among the powers of Europe in the late nineteenth century. Great Britain, Germany, France, Japan, and other nations each controlled trade in Chinese ports, and they alone could dictate the terms of trade. The attempt by the United States to open markets by what was called an "Open Door" policy, but this too, was only a means of opening Chinese markets to Western goods on terms imposed by Western powers.
Imperialism in all forms usually involved "cultural" imperialism, where the imperial power attempts to impose, usually in the name of modernity and charity, aspects of its own culture on people around the world. This has proven especially true of religion.