It’s all really simple and makes a lot of sense [yet is still very powerful]
the top set of buttons, orco, uv, object, glob, win, nor ref … determine what the texture coordinates are generated from
UV: uv coordinates
obj: [in the text box goes the name of the object]
glob: global coordinates, texture stays put in space as object moves
orco: original coordinates, texture stays put on object as it deforms and moves
sticky: not very useful, they are per-vertex uv coordinates which cannot be modified. They are created by pressing the make sticky button in the edit buttons iirc
win: window coordinates
nor: surface normal
ref: surface reflection vector
the sets of 3 numeric inputs on the right are for the offset and scaling in each axis of the texture [to rotate the texture you’d probably want to use an obj-mapped texture, which also is easier to animate]
the Flat tube cube and Sphere buttons are from what I can tell only used when mapping images. They define how the image is wrapped around the object [how a 2d object is put on a 3d surface]. The docs cover this part pretty well
hrm, is blender.org and blender3d.org down? [if they weren’t I’d link to the page mentioning the effects of those buttons, with pictures]
the last 12 buttons I think are the coolest.
The top row is for the x axis, the second row for the y axis, and the third row for the z axis. The buttons determine which input axis goes to that axis. So, the default is that the x axis coordinate goes to the x axis as you’d expect. These buttons allow you to flip textures as you’d like.
For example, the default settings do not make for a very interesting result with a normal mapped blend texture. You can map it so the blend is on the front facing the camera with X Y [Null] and on the back, on the edges of a mesh with Z Z [Null]