The recipe
The easiest place to see Dorian is on a piano: play every white key from D up to D. That's D Dorian. The notes are identical to C major's white keys, but the scale is built around D instead of C, which changes the interval pattern from whole-half-whole-whole-half-whole-whole (Ionian) to whole-half-whole-whole-whole-half-whole (Dorian). The position of that interior half-step is what defines the mode.
Every mode of the major scale works the same way. Start on the 2nd degree, you get Dorian. The 3rd gives you Phrygian. The 4th gives Lydian. Same seven notes, seven different centers, seven different sounds.
What the raised 6th does
In natural minor, the 6th sits a half-step above the 5th and tends to fall down to it. That downward gravity is part of what gives natural minor its weight. Dorian raises the 6th by a semitone, putting it a whole step above the 5th. The pull is gone. The scale still has a minor 3rd, so it still reads as minor, but it doesn't feel like it's grieving.
Where you've heard it
Scarborough Fair, in E. The raised 6th (C♯ instead of C natural) is audible in the melody and is the reason the song doesn't sound funereal even though it's structurally minor.
"So What" by Miles Davis. The A section vamps on D Dorian for sixteen bars. Bill Evans's piano voicing under that vamp (stacked fourths) is one of the most copied sounds in jazz, and it's just Dorian harmonized vertically.
"Eleanor Rigby". The Beatles in E Dorian. Beatles scholars including Allan Pollack and Walter Everett all classify the song this way, pointing to the raised 6th (C♯) in the string accompaniment.
Mad World, both the Tears for Fears original and the Gary Jules cover. The verse chord progression is Em-G-D-A. That A major chord contains C♯, the raised 6th of E. The chord progression is where the Dorian quality lives more than the melody.
Telling Dorian apart from the other minor modes
Dorian shares a minor 3rd with natural minor, harmonic minor, melodic minor, Phrygian, and Locrian. The disambiguation is in the surrounding degrees.
Versus natural minor: the raised 6th. If a minor melody hangs on the 6th and that 6th sounds bright rather than mournful, you're in Dorian.
Versus Phrygian: the 2nd degree. Phrygian's 2nd is a half-step above the root and gives the mode a flamenco color. Dorian's 2nd is a whole step away and stays neutral.
Versus melodic minor: both raise the 6th. Melodic also raises the 7th. If the leading tone pulls hard to the tonic, you're hearing melodic. Dorian leaves the 7th flat, which is part of why the mode feels modal instead of pointed at home.
Why pop music likes it
Dorian doesn't pull toward a dominant chord the way natural minor does. A song in D natural minor typically uses A or A7 (the functional dominant) to get back to D. A song in D Dorian usually skips that move and alternates Dm with another minor or quartal voicing. That avoidance of the dominant is what makes Dorian feel modal rather than functional, which in turn is what lets a four-chord pop song stay interesting without resolving anywhere in particular.
How Aubel handles it
The Scales game starts with major, natural minor, and harmonic minor. Dorian is fourth in the canonical progression, unlocking after the starter pool stabilizes. By the time you meet it, you've already trained the minor-3rd-versus-major-3rd distinction, which is what Dorian leans on for its identity.