U and V are axis names, like X and Y but UV space is only ever two dimensional and conceptually seperate from the X and Y that exists along side Z in three dimensional space. Now, you can describe say, a cube in XYZ space, but you can also … flatten it out like unwrapping a present, or more accurately like taking apart a cereal box and making it lay flat.
On the left, the cube exists in X, Y and Z. On the right, that same cube is now mapped to U and V. Let’s say you wanted to make that cube a six sided die. By being able to translate the 3 dimensional geometry to the 2 dimensional space, I can now paint an image in photoshop or the like and put dots on faces of the die, and the software can take that part of the image and show it on the face in 3d space. Does that clarify UV in that context?
To be fair, UV to XYZ space is something that drives me CRAZY and I joke the UV stands for Ur’Ventorok, Elder God of Non-euclidean Spaces who wants to make us all gibbering lunatics.
Editing Note: Ok, I think there are cases when UV space isn’t strictly 2 dimensional, and in those cases it’s UVW like XYZ, but I’ve been a CGI hobbyist for close to five years now, and have never needed a W axis yet. I may be a know it all, but I admit I don’t know everything.