A flow field that moves like liquid. Where ordinary noise gives you blobs that swell and shrink, this gives you swirling currents that carry things along without ever piling up or draining away.
That property is the whole point, and it comes from a piece of mathematics called the curl. If you take any field of values and ask, at every point, how much it is rotating rather than how much it is flowing outward, what you get back is guaranteed to have no sources and no sinks. Nothing can accumulate. Feed that to particles and they behave like smoke or water rather than being sucked into invisible drains.
Working it out means measuring how the underlying noise changes as you step a little in each direction, twelve times over for every pixel. That is expensive, so leave octaves low unless you need the detail. intensity sets how strong the swirling is.