All literature, including poetry, can be interpreted using different methodologies. For example, if you were to analyze William Wordsworth's poetry, you might do a biographical analysis of his life to try to connect his actual experiences, such as witnessing the French Revolution or his love of nature, to his poems. You could also do a source study and try to understand what earlier poets, such as Milton, influenced him. Or you could examine the way he treats women in his poems, called feminist analysis.
In literary stylistic analysis, also called New Criticism, you don't look at the life or times of the poet. Instead, you focus entirely on the text—the words on the page—that are right in front of you. Here you are examining how the poet expresses his theme and tone through the stylistic devices he uses: his imagery, his use of rhyme, alliteration, assonance, point of view, etc. It means trying to squeeze all possible juice out of poem simply based on the words in the poem and how they are arranged, without regard to the poet's life or times.
Take one example, "I Wandered Lonely as a Cloud," a poem by Wordsworth. You would look, for starters, at the rhyme scheme; the central image of the daffodil (what is it likened to, why is it personified, and how does it make the narrator feel?); the use of time in the poem (what are the effects and what is the thematic point of the time shift in the last stanza?); and the impact of the simple words used, and how they convey the tone of joy Wordsworth wishes to express. In a close examination, you would understand how carefully he crafted this seemingly spontaneous and simple poem.
The term "New Criticism" was coined in the 1930s by, among others, the editors of the influential journal Scrutiny. Focusing on the text itself was a way to correct what some scholars saw as a distorted emphasis on biographical and source study criticism.