Do you know what a major scale is? If so, the Dorian mode is the same scale but starts on the second note instead of the first. Imagine a C-major scale because it has no flats or sharps:
C-D-E-F-G-A-B
Now, instead of starting on C, start on D:
D-E-F-G-A-B-C
It's the same notes in the same order, but since the root note is now D, it's the D Dorian scale. Why isn't it D major? Because D major looks like this:
D-E-F#-G-A-B-C#
Why is it different? Because major scales have intervals (do you know intervals?) that look like this:
whole-whole-half-whole-whole-whole-half
Ans the dorian scale looks like this:
whole-half-whole-whole-whole-half-whole
If you don't know what an interval is, look at the fretboard. Each single fret is a half step. Two frets is a whole step. To further complicate things, a single step is also called a minor second and a whole step is called a major second. Why? Well...
This is where I found music to be utterly confounding until one day it clicked. Music majors speak in the language of music and may go back and forth between half step and minor second depending on the context. The reason i thought about writing a book is because I never found anything that explained all of this simply, and that tends to be something I'm good at.
Oh, and the piano mentioned earlier? It makes perfect sense when you look at it with the concept of intervals. The black keys are spaced the way they are because that's how musical scales work:
From Wikipedia: