The term was first used as a variation of artistic impressionism, but did not really catch on. What it really is is still not entirely clear, as you can see from the links below, which discuss various definitions and various writers. The Oxford dictionary defines it as A literary or artistic style that seeks to capture a feeling or experience rather than to achieve accurate depiction. In describing the works of Tillie Olsen, Kathy Wolfe stated that they were an innovative combination of third-person narrative, dialogue, and interior monologue that reveals her characters’ thoughts, memories, and perceptions, which seems a pretty good attempt to give a definition. Suffice it to say that there are many variations of this definitions as you will see from these links and the books referenced. It encompasses a wide variety of authors, from Henry James, Gustave Flaubert and Joseph Conrad to Dorothy Richardson, Ford Madox Ford, Virginia Woolf, Jean Rhys and Olsen.
Books on Literary Impressionism
Todd K. Bender: Literary Impressionism in Jean Rhys, Ford Madox Ford, Joseph Conrad, and Charlotte Brontë
Rebecca Bowler: Literary Impressionism
Maria Elizabeth Kronegger: Literary Impressionism
Jesse Matz: Literary Impressionism and Modernist Aesthetics