The idea is that by layering enough of these on top of each other, you can make a high quality visual representation not bounded by geometry.
Think of them like brush strokes in mid air versus a sculpture.
There has been a big explosion of interest in the area since this release of https://repo-sam.inria.fr/fungraph/3d-gaussian-splatting/ which proposed a way to generate the point cloud data from photographs in a way that is procedurally a lot like photogrammetry. Hundreds of research projects have spawned off of that paper.
That said, Gaussian splats are based on very old papers that do have use in Hollywood. The closest example is radiance caches for Renderman.
This would store points in space with very similar information to a splat, then interpolate between them to provide things like bounce lighting.
The first Pixar film to use this throughout was Up.
What are some examples of those representations?
They just have a higher up front cost to make than Gaussian splats but are infinitely more directable.
Ultimately the ability to control everything at a micro and macro level is what film wants, not cheap rendering.
Gaussian splatting represents a scene a cloud of 3d gaussian ellipsoids, with direction-dependent color components (usually represented using spherical harmonics) to deal with effects like reflections. The "Gaussian" part is important, because gaussian distributions are easy to differentiate, making it possible (and fast) to optimize the positions, sizes, orientations, and colors of a collection of Gaussian splats to minimize the difference between the input photos and the rendered scene. This optimization is usually done by starting with the same 3d point clouds and camera poses estimated using the same or similar tools as traditional photogrammetry (e.g. COLMAP), and using this point cloud to place and color your initial Gaussian splats. One of the key insights in the original Gaussian splatting paper was the use of some heuristics to determine when to split a splat into smaller ones to provide higher detail over a given area, and when to combine splats into larger ones to cover uniform/low detail areas.
The nature of Gaussian splats being essentially fancy point clouds means that they can't currently be easily integrated into existing 3d scene manipulation pipelines, although this is rapidly changing as they gain popularity, and tools to convert them into textured meshes and estimate material properties like albedo, reflectance, and so on do exist.