Imperialism (in the Marxist-Leninist sense) happens when the bourgeoisie of one country expand their influence and control into a country which hasn’t yet developed capitalist relations. They proletarianize that country, but do so without the country developing its own local bourgeois class. Lenin particularly emphasizes the role that monopolization plays in this process. I can describe it using less jargon if that would help.

The imperial core is the collection of countries which have historically engaged with and benefited from this practice. So, in a very broad sense, the US, Canada, Europe, and Australia. Plenty of nuance there, but that’s the gist of it. Colonialism really set up the footprint for imperialism to take hold.