In this introduction, Eagleton sets out to describe what literature is prior to defining what literary theory is. Since literature is literary theory's object of study, it would make sense to pin down exactly what literature is.
He begins by trying to establish if literature is defined as fiction as opposed to fact. Since the question is too wrought with contradictions, he moves on to discussing the Formalists and New Critics who sought to define literature in purely structural and formalistic terms. But he debunks these seemingly objective theories of literature by giving examples showing that what is poetic to a certain group of people at a certain time in history may not be poetic (or literary) to other groups at other times in history. In addition, Eagleton has trouble dealing with definitions of literature purely in terms of linguistics. Where is the human element? Not to mention, he indicates that "literariness" ought to be about content as well as form. A text might employ allegory quite effectively but don't the themes and content lend credibility and significance to the form of the allegory?
Eagleton's determination is that there is no set criteria of literature as an unchanging subject of study. Thus, 'literariness' depends upon social and historical context; it is always changing. History and culture play a role in how a social group and/or its individuals make value-judgments about what literature is, and what makes it good literature. This incorporation of culture, history, and ideology is where Eagleton's Marxism comes in. Eagleton suggests that our value-judgments can be subjective (private and individual) at times but often they are linked to sociological realities and biases: ideologies.
(Marx was an historical philosopher. He believed that people have individual will but they are largely determined by social and economic forces. Eagleton links this determination to the ways we approach literature.)
I do not mean by 'ideology' simply the deeply entrenched, often unconscious beliefs which people hold; I mean more particularly those modes of feeling, valuing, and perceiving and believing which have some kind of relation to the maintenance and reproduction of social power.
George Orwell's allegory of Animal Farm functions well not just because of its structure but because of its significance to history: The Russian Revolution. Going by Eagleton's analysis, Animal Farm will continue to be relevant as "literary" as long as readers continue to get something literary out of it; namely, the structural and thematic importance of the allegories about power struggles, fascism, and revolution -- described in literary ways.
Combining Eagleton's discussions on defamiliarization (the Formalists) and his Marxist lens on literariness, texts like Animal Farm will be read as literary if they present a relevant (or socially significant) theme in a literary (unfamiliar - differing from everyday speech) way. Animal Farm is an easy example of this. However, this is not to say that Eagleton was implying that, to be literary, a work must note some social or even Marxist theme. He just uses Marxist philosophy to note the impact of historical context: how people at different times in history will have different judgments on what literature is. The social power structure of a given society, at a given time in history, will affect what is considered literary at that time: by those who believe in the structure or by those who rebel from it.