Light Echo
What we’re seeing here is what’s called a light echo. The dust cloud around the star is old, probably thousands of years old. When the star suddenly brightened, it sent out a flash of light that moved outward, illuminating the pre-existing cloud from the inside out.
In the video it looks like the cloud itself is expanding (you can see motion of individual structures), but that’s an illusion. Over just a few years the structure wouldn’t be seen to expand at all; we’re just seeing different structures (or different parts of the same structure, like filaments or compressed regions) as the flash of light moved through the nebula.
(Source: Slate Magazine—Bad Astronomy Video: The Bizarre Eructation of V838 Monocerotis)