An Anti-imperialist is an opponent of imperialism, a stance often taken by subjugated people around the world. Anti-imperialism has its roots in the early days of imperialism, around the middle of the 19th century, when "imperialism" was a newly invented word and political concept.
The effect of imperial powers on native cultures was addressed briefly after World War I, and a bit more so after World War II. The breakdown of European empires around the world allowed for a venting of anti-imperialist views, often taking the form of nationalism.
Empires can also be anti-imperialistic to each other. The Soviet Union was seen as imperialistic by America, so anti-imperialism can be empire specific. In today's day and age, anti-imperialism is often attributed to America's increasing presence in economically sensitive areas around the world.