How it works
The CustomizedUV pins pass through the texture coordinates (UVs) in the mesh by default. Then when you place a Texcoord node in a pixel shader input (like BaseColor), you are still getting the mesh's texture coordinates. However, if you do something in CustomizedUV0 and then use Texcoord 0 in the BaseColor input, you will get the modified UV value. Note that Texture sample nodes use TexCoord 0 by default.
Shader Model 5 on PC can use 8 custom UVs, while OpenGL ES2 on mobile can only use 3.
Here is an example, the original material is mapping a texture using world space y and z.
This material is doing the same thing, the logic in Customized UV 0 is passed through as Texcoord0 to the BaseColor pixel shader input. However, the calculation for Texcoord0 was done in the vertex shader.
The Texture Sample node has an implicit TexCoord0 node inside.