In "Mr. Wordsworth," Hazllitt is talking about Wordsworth's use of common people and nature in his poetry. Wordsworth's themes and characters are more commonplace than his style. However, compared with his predecessors (most notably those like Alexander Pope of the Neoclassical period), his style is closer to ordinary language and his themes, which can be transcendent, develop from ordinary people and events.
Wordsworth often wrote about ordinary, rustic scenes and characters. In "The Solitary Reaper," he writes about a common Scottish girl singing in the countryside. His poems are not about kings and queens. They are about the self and the individual's contemplation of his/her own feelings in relation to nature and human history. His poems aspire to intense feelings and abstract truths, but they do so by beginning with common human and everyday natural events/things.
Wordsworth looked for impassioned, enlightening experiences through human experience. He, and other Romantic poets, looked upon the imagination as something more than a daydreaming or creative medium. For the Romantics, the individual imagination was a conduit of intuition to the sublime.
Hazlitt argues (albeit with some criticism of Wordsworth's narrow thinking and egotism) that Wordsworth embodied the spirit of the age (Romanticism) with his focus on the individual human experience and the imaginative connection between human experience and nature.