The basic definition of an empire is when a state rules over another nation or state. This definition can get a little blurry due to "national" aspect but it's probably the best definition. Marxism, (specifically Lenin's developments) adds that economic control through the export of finance and industrial capital to other nations is imperialism and that it is a natural stage in capitalism.

So the US is an empire because of it's colonialism, but also because of it's control over the global capitalist system which comes not (specifically) from its military at the behest of the nation, but through its export of capital by its capitalist class.