It's similar to how the terrain texture blending works. In fact, that's one of the most common ways to control which textures are where on the terrain - by changing the vertex color values - and is similar to what we do with our terrain.
For more specific examples, it allows you to do stuff like having, say, a brick floor material, and then additional texture maps/materials that blend in as needed like, say, water and snow.
So you'd have your brick floor on your ground, and then by painting vertex color values, can dictate spots to have water and snow accumulation, letting you pick specific parts of the ground to have water puddles, or snow piles.
This can be extrapolated to practically anything. Stone wall with greenry growth or grime, cracks in concrete, etc. Because you select what parts of the surface have the various blends, it allows you to take a common material, and apply minor changes via the blends, adding lots of detail as needed and also helps combat the 'repeating texture' effect. All in all, a very powerful tool for artists to work with to make their scenes unique and interesting.
One of the advantages this method offers is a single material, but nearly infinite variations in surface. This is especially useful in cases where you have a bunch of prefab parts to make buildings. Obviously if you just used the same peices with the same textures, it becomes really repetitive, but having a bunch of different textures uses more memory and adds draw calls. So you could go in there and using one material, paint grime in various spots, breaking up the repetition without tons of additional memory use and draw calls.
The thing that separates it from a simple texture overlay is you can use the normal maps as a contributor, so as the video shows, is when he paints the sand/water, it accumulates in between and at the edges of the tiles first, which is more realistic, and then the flat surface areas. You can also mix and match a few different materials, or have it offset the verts in the very shader to have sand accumulation actually raise off the surface for more depth, etc.
Should note the vertx painting approach specifically (as oposed to a splatmap, which would be a 5th texture where you reference rgba for your blend ops) does require a higher than normal polycount for lookup, pretty much by definition.
So you need to add more vertexes for it to work smoothly? Lets assume you have a wall that is juts 4 vertexes, how you gonna blend that? I wonder how it works that you have one material? I mean you have multiple ones like with the terrain. It looks a bit like the megatexture approach where you can paint it like you want and in the end it gets baked to one megatexture.