The best known of the Lake Poets are William Wordsworth, along with his sister Dorothy, and Samuel Taylor Coleridge, with Robert Southey coming in at a distant third. All three were, while they resided in the picturesque Lakes District, part of the first-generation Romantic movement (note that it wasn't until after the second generation that the association between the word romantic and our modern concept of romantic love arose.) They believed strongly in the value and importance of nature to poetry and to the soul, and were in rebellion against the strict rules and high formal language of the dominant literary movement of the time, neoclassicism. In contrast, they deliberately used the simpler language of common folk and wrote looser, less strictly defined verse forms about more personal matters. Where the focus of neoclassicism was always on the great exploits of heroes of the past, Romanticism focused on the experience of the self alone in nature.
It's not surprising that a group of Romantic poets wound up in the Lake District. It's an exceptionally beautiful place, full of vivid greens and eery mist and brightly-coloured flowers like the ones that inspired one of Wordsworth's best known poems, “Daffodils”. It's mountainous country, but with mountains such that you can start hiking before breakfast, reach the very peak of one and be back in time for afternoon tea. It's not strictly wild country, but the winding dry-stack walls and stone houses are so old they seem a proper part of the landscape, and it's easy to wander off a bit into a field or wood and lose yourself completely in the beauty of it all, as the poets were wont to. On the downside, the weather is a near-perpetual misty drizzle, so if you ever decide to visit the Wordsworth's cottage in Grasmere (and you should, it's a very interesting place and you can get a fascinating tour) or Coleridge's place in Keswick, be sure to bring a decent jacket.
The poets themselves were just as interesting as the landscape. For most of their stay in the Lakes District the Wordsworths were engaged in a sort of social experiment. They had a small cottage in a rural area, a garden, and a few animals, and their goal was live a simple lifestyle, remaining close close to nature and sustaining themselves purely through their garden and animals and perhaps a small amount of funds from William's writings. William Wordsworth was a very thoughtful, philosophical poet; many of his poems double as explanations of his rather lofty ideas. To him, nature was a spiritual nurturer and an inspiration to the soul, and the ability to truly appreciate it was a sign of a childlike purity of soul. As he outlined in his “Immorality Ode” (full title “Ode: Intimations of Immortality from Recollections of Early Childhood”) and more partially in “Tintern Abbey” (full title “Lines composed a few miles above Tintern Abbey on revisiting the banks of the Wye during a tour, 13 July 1798” - Wordsworth had a bit of a thing for long titles) he believed that children enter the world with something of the glory of heaven clinging to them, which tends to fade as they grow older, and should be held onto at all costs.
William's sister Dorothy deserves mention here as well, for while people don't traditionally think of her as a poet her handwriting can be found alongside Samuel and William's in their original manuscripts, and it's clear from her extensive diaries that she had an important hand in both the inspiration and the planning of the others poetry. Her writings also make it possible to make direct connections between poems and events in the poets' lives - for example one of her diary entries describes a particularly beautiful field of daffodils blowing in the wind.
Coleridge was by far the wilder of the two. He wrote surreal and fantastical poems like "The Rime of the Ancient Mariner" and “Kubla Khan”, the second of which was based on a vision he had in an opium-induced dream and is unfinished because he was interrupted partway through the writing process and could never remember the rest of the lines afterwards. He shared Wordsworth's idealization of youth and detested the schoolhouses of his own youth (these were genuinely detestable places where boys were sent away from their families to sit still for extremely long hours learning Latin and mathematics in crowded rooms.) He outlined the ideal childhood he desired for his own baby boy in “Frost at Midnight”.
Eventually the Lake Poets dissolved, Wordsworth going on to abandon Romanticism and become poet laureate and Coleridge descending further into his opium addiction. Their works, however, live on and have continued to inspire admiration up to this very day.