Texture1D and Texture3D, how ?

I can imagine 1d texture, just simple a line with only x or y coordinate but what is a 3d texture and why,when,where should i use them both ?

An example for a 1D texture would be to use it in thermography. It can also be used to texture mountains where the top is white and the bottom are greener. It can also be used to do palletted texturing.

A 3D texture can be used as a noise map. See RenderMonkey from AMD, it has some examples. They also make use of 1D textures for other things.

A 3D texture is a volume, you can also directly color your model with that by imagining the the model intersects the volume and you use the color at the intersection points.
A 3D wood texture for example can store the rings of the woods and by intersecting it with different meshes, you get nicely textures wooden items, all with the same texture (also this yould be done with a procedural 3D texture that uses a small 3D noise texture…).