Coleridge, in Biographia Literaria, differs with his friend Wordsworth chiefly about the appropriate kind of language to use when writing poetry.
In his Preface to Lyrical Ballads, Wordsworth expresses the view that the language of poetry should essentially be no different from that of prose (allowing, of course, for the purely technical fact that poetry possesses meter and rhyme). Wordsworth therefore views with disfavor a specific kind of "poetic diction," or special words and expressions traditionally used in verse. He quotes Thomas Gray's "Sonnet on the Death of Mr. Richard West," considering such lines as "In vain to me the smiling mornings shine / And reddening Phoebus lifts his golden fire" as stilted and valueless. For Wordsworth, poetry must use a simpler kind of English, especially the language of people from the countryside.
Wordsworth's plan was basically to effect a revolution in poetry. Though it's sometimes necessary to make sweeping changes in order to start a new movement—in this case what we know as Romanticism—Wordsworth perhaps went too far. It's easy to see why Coleridge, though he collaborated with Wordsworth on Lyrical Ballads, would disagree with him on this point. The poem Coleridge is chiefly known for today is, of course, The Rime of the Ancient Mariner. Though simple and straightforward in its language, the poem uses deliberate archaisms and a style reminiscent of the folk ballad, not the sort of wording that we would see in, say, an essay or a novel.
In Biographia Literaria, Coleridge attempts to explain why the ideal poetic language cannot be dependent on the rigid prescription given by Wordsworth. For Coleridge, there is nothing especially superior or preferable about either prose-like diction or the language of rural people. What makes a poem great is independent of such factors.