It’s quite hard to explain without image reference, but I’ll give it a shot.
By default, the UV input node is just two gradients. One is a gradient from Right > Left in the ‘Red’ channel, the other is a gradient (black to white) from Top > Bottom in the Green Channel. The term ‘gradient’ is slightly misleading, since they aren’t gradients, they’re actually just a representation of a sequence of 2D Coordinates.
That’s why when you place a TexCoord node down in the material editor, you’re given the funky red/yellow/green looking node. Although it looks like a gradient, it’s actually just purely numbers. It’s just a gradient from 0-1 in X (red), and 0-1 in y (green).
Now, Textures map each pixel to a specific UV-coordinate. In a texture that’s 10px * 10px, the top-left pixel in the source texture will be at UV position 0, 0. The one at the bottom-right will be at position 1, 1. All the pixels in between will be at their respective positions and have a coordinate relative to their position in the texture. Simple so far yah?
Now imagine that I change the UV input by changing the value at (1 1) to (0 0). I haven’t changed the texture yet at all, all I’ve done is change the values of the UV’s. When I send this input to the texture, the pixel on the texture that was originally at 0, 0 will now ALSO appear at 1, 1. AKA, the pixel at the top-left will also be displayed at the bottom-right.
The World-Position node gives you the world-position of a specific pixel. World-Position you can also think of like a gradient, going from zero up to some large number, based on where the pixel is in the world. You can divide this by a certain number to make the scale smaller, and plug that into the UV’s to create the same kind of ‘gradient’ of numbers in 3D-space.
Hopefully that explains it well enough. The best way to think about it is think of UV’s as a gradient of numbers or coordinates. Manipulating those coordinates changes the way the texture appears.
There’s a great tutorial on ImbueFX.com, called ‘Colour Indexing’ which is Free! I highly recommend watching it, it should explain everything https://www.imbuefx.com/downloads/vfx-quick-tips-color-indexing-in-udk/