What does William Wordsworth argue in his preface to Lyrical Ballads?
Wordsworth argues many things, one of which is that he cannot argue a proper defense of his poetry, "Poems so materially different from those [of] general approbation," in a space proportionate to a volume of poems the size of Lyrical Ballads. In this Preface, he does argue two central points about his theory, his aesthetic, of poetry. One argument is the purpose of his poetry; the other is the style of his poetry.
Wordsworth asserts every poem in the Ballads has a "worthy purpose" and that purpose is that through his poetry we might "discover what is really important to men." Thus he echoes the ancient idea of an inspired poet who brings enlightenment to humans. Wordsworth expects to accomplish this by poems that are inspired by nature and that have language "associated with the great and beautiful objects of nature." His motive is to "counteract" the influence of poems that are "deluges of idle and extravagant stories in verse."
His other argument is to defend the style of his poetry. While Aristotle's poetics, held to by every generation up to Wordsworth, advice characters who are noble, though not unflawed, and subjects that are great and important and of weighty substance, Wordsworth's new poetics advances the value of common, everyday characters from pastoral, "rural life" and natural lifestyles. "Low" language describes low subjects of those who face elemental survival with "passions of the heart [that] find a better soil." Wordsworth concedes that the language of rural living must be purified and made aesthetic before it can be used, yet claims if has intercourse with nature:
["Low" language must be] (purified indeed from what appear to be its real defects, from all lasting and rational causes of dislike or disgust) [though it is] incorporated with the beautiful and permanent forms of nature.
In summary, Wordsworth asserts that he writes with the dual intention of  counteracting the base turn literary art has taken that depends on gross emotionalism and sensationalism and  idealizing the rural, or pastoral, qualities of life and commonplace struggles along with the commonplace, sometimes vulgar and defective, expressions of language and thought. Coleridge came to disagree with him because, as Coleridge points out, it takes a poet to turn vulgar reality to the poetic commonplace though Wordsworth denied doing so materially discounted the commonplace low poetic diction he strove for. One of the premiere examples of Wordsworthian success in this new poetic is The Ruined Cottage.
Wordsworth makes several crucial points about poetry in his preface to Lyrical Ballads. He suggests that the most authentic poetry is that which engages with everyday experience, particularly in nature. This theme is reflected throughout the book of poems, where he emphasizes the power and beauty of the natural world, free from human artifice. Wordsworth also says that good poetry should speak to emotion, reflecting a spirit of deep and profound meditation. He claims that many devices used by poets (e.g. personification, off-kilter wording, and so on) distracted readers from the feelings that should lie at the heart of the poem. So he proposes to strip poetry down, so to speak, to its basics, in a language that can be understood and appreciated by a wide readership. The crux of his approach to poetry, especially in Lyrical Ballads, is summarized in the following passage:
The principal object, then, proposed in these Poems was to choose incidents and situations from common life, and to relate or describe them, throughout, as far as was possible in a selection of language really used by men, and, at the same time, to throw over them a certain colouring of imagination, whereby ordinary things should be presented to the mind in an unusual aspect...