I think we generally mean those countries that benefit from imperialism because of unequal exchange or financial institutions like the IMF and World Bank enforcing a state of destitution and exploitation of what we call the imperial periphery. You can find a lot more precise and well thought out political analysis in these terms if you read up on World Systems Theory. The important aspect is that there is a flow of wealth from the periphery into the core.

It's a very relevant concept because the countries in the imperial core have working classes that, despite being exploited themselves, have a great deal of resistance to international solidarity because they live lifestyles that are only possible due to the exploitation of the periphery. The implications are broad, and people here range from those who think that the working classes of the imperial core are still capable of surpassing that bias and carrying out a fair distribution of global wealth, to the Third Worldists who believe that the revolution can only meaningfully come from the imperial periphery, else it would capitulate to imperialist interests and fail to move past capitalism.

My personal take is that it doesn't matter too much what is or isn't possible in the imperial core, the task at hand is the same for us: agitate, educate, organize to demolish the capitalist imperialist system, our comrades in the periphery will have more space to carry out their revolutions that way.