What is ideology? For Marx, it amounts to false consciousness. We have rationalizations that justify our place in the world, our economic privilege. For those who have benefited from economic inequities built into capitalism, there is a strong incentive to justify the inequities in terms of one's own effort, or the effort of one's family or people. Furthermore, we may willfully or unconsciously ignore the forms of labour that go into the products we purchase. We may not see, for instance, that they are made with exploited labour, preferring to focus on the low price. Ideology is what justifies class difference. The state functions to keep all this in line in what Louis Althusser will later will call the Repressive State Apparatus (RSA). Think of the army, the police, the penal system, etc.
Under critical theory, the concept of ideology becomes more sophisticated. Marx assumes that there is a reality that we're deluded about. All we need to do is uncover the full picture. And, of course, we would also need to address the draw that privilege and wealth bring. But it is basically a matter of showing reality for what it is.
What if it doesn't work like that? What if there is no reality at the bottom of it all, to become clear about? Althusser thinks that Marx was right that capitalism is essentially repressive, but that we need to be clearer on how it works. It is not just a matter of the state enforcing inequality, but rather that we enforce it for ourselves through the way we tell our stories about the world. Althusser calls this the Ideological State Apparatus (ISA). Think of churches, families, schools, universities, the media.
We come to think that we are free beings who choose everything, from commodities to our own beliefs. We are free "subjects", but in fact we are "subject", that is, subjected. In fact, our social order inclines us all to be part of this ideology. This includes Althusser himself, and he knows it. But that doesn't detract from the idea that subjectivity doesn't just show up, but is constructed based on these stories we use to justify our position in society. In fact, for Althusser, subjectivity is set even before we are born:
it is certain in advance that it will bear its Father's Name, and will therefore have an identity and be irreplaceable. Before its birth, the child is therefore always-already a subject, appointed as a subject in and by the specific familial ideological configuration in which it is 'expected' once it has been conceived. (Althusser, Lenin and Philosophy)
Althusser calls ideology "the imaginary relationship of human beings to their real conditions of existence." That's not reality of the sort mentioned above, the Marxian version, but rather it refers to the way in which we justify the unequal conditions we put up with. The question after the most recent election that many Democrats asked (and never really did answer) was "why do people vote against their interests?" The answer in terms of ideology is that their votes are not seen as being against their interests. They do not see their (or their neighbour's) economic condition as being one which implicates contemporary economic policies. Those policies are seen as agents for good, by encouraging engagement in the economy. So, poverty is seen as a personal failing rather than a class issue.