And originally, the culture or 'civilisation' of an empire, more surely even than trade, followed its imperial banner. That culture is commonly portrayed as an inevitable lagniappe, or perhaps quid pro quo, for the economic and military advantage enjoyed by the empire. It is also usually portrayed as, on balance, a Good Thing. This is at least partly because the civilisation of the empire tended to produce people opposed to the excesses of imperialism, or to imperialism holus bolus. Cultural imperialism' is rather more complicated - although everyone knows what it means.
Cultural imperialism is the conquest of one culture by another.
No, this is not strictly the case. Cultural imperialism is a term rarely, if ever, employed in discussions of Great Britain, France, China, Japan, India - not to mention the Union of Soviet Socialist Republics. The answer which is accepted these days is that 'the consciousness' of people is conquered, colonised. Their mental universe is invaded and transformed from one, presumably indigenous and positive state, to another, presumably foreign and negative. We are talking mind control here.