In his important 1983 book Literary Theory, Eagleton argued that literature and literary criticism is political but pretends not to be.
Ideology, in Marxist terms, (and Eagleton at the time was a Marxist) is a set of ideas that provide justification for the ruling classes having most of the money and power in society. Ideology is a false story the rulers tell that mystifies (puts a mist or fog around) reality, so the mass of people don't understand what is really happening to them.
In his book, Eagleton posits literature as a construct. There is nothing real, as in the physical laws of nature, that defines certain books as literary works. Further, literature as a field of study is a response to certain political needs of the end of the nineteenth century. More and more working class people and women across social classes were attending college, through a growth in night schools and other ventures. Most of them could not read Latin or Greek, which was the backbone of an upper-class male university education. Therefore, "great works" in English literature were substituted for classical authors. It was easier to teach Chaucer or Thomas Hardy than teach people Latin and read texts in the original language.
By studying literature in a vacuum, whether through the New Critical ("text only") approach or through the semiotics or deconstruction schools that were in vogue when Eagleton was writing, literary scholars were approaching literature as if it were timeless and apolitical. Eagleton argues that apolitical approaches support the ruling class's ideology. Implying that literature is apolitical means teaching that social systems privileging the rich in most literature are "natural" and can't be contested. Instead, Eagleton says, literature should be approached as political, whether you are conservative or liberal, because it is inherently so. To argue otherwise is to try to spread a false mist or ideology over its content.
Today, we do tend to approach literature as political and ideological far more than was the case in the early 1980s. Eagleton's book was more startling when it was first published than it is today.