Diatonically,
The simplest way I can explain in a physical sense is to use a Piano.
Both are in concert C.
Middle C as a reference point and the C scale using just the white keys renders CDEFGAB octave C.
So now knowing this formula in relation to a guitar neck and to how a Major scale is built, one knows all the Modes.
Converting the notes to a numbered format, then you would have 12345671.
6 string root example
Ionian
12345671
Dorian
23456712
Phrygian
34567123
Lydian
45671234
Mixolydian
56712345
Aeolian
67123456
Locrian
71234567
"...So when guys say know your modes from every "position". What exactly does that mean?..."
Know one position for all positions. IOW the mathematics and fundamentals are the same for every key in
"every position"
It is here and side-by-side one can plainly see where ALL the sharp's-#'s and flat's-b's are in comparison to the One...
Ionian
|--1--|----|--2--|-----|--3--|--4--|----|--5--|-----|--6--|-----|--7--|--1--|
Dorian
|--2--|----|--3--|--4--|-----|--5--|----|--6--|-----|--7--|--1--|-----|--2--|
Compared to the One by simply placing it underneath to see the intervals.
The 2 scale or Dorian Mode has a flat 3rd and a flat 7th easily seen here.
This is how the 2 Dorian scale has a b3 & a b7
(This also falls under the Circle of 5th's mystery know how many sharps & flats in a scale.)
Ionian 1. |--1--|----|--2--|-----|--3--|--4--|----|--5--|----|--6--|-----|--7--|--1--|
Dorian 2. |--1--|----|--2--|-b3-|------|--4--|----|--5--|----|--6--|-b7-|-----|--1--|
Now that we know EVERYTHING is actually
compared to the 1, one can easily figure out the formulas to all the seven modes.
The 3 Phrygian scale easily seen has a b2, b3, b6 & b7
1. |--1--|-----|--2--|-----|--3--|--4--|----|--5--|-----|--6--|----|--7--|--1--|
3. |--1--|-b2-|------|-b3-|-----|--4--|----|--5--|-b6-|-----|-b7-|-----|--1--|
Looky here, the 4 Lydian scale has a #4
1. |--1--|-----|--2--|-----|--3--|--4--|-----|--5--|----|--6--|----|--7--|--1--|
4. |--1--|-----|--2--|-----|--3--|-----|-#4-|--5--|----|--6--|----|--7--|--1--|
Mixolydian with a b7 (Known as the Dominant 7th)
1. |--1--|-----|--2--|-----|--3--|--4--|-----|--5--|----|--6--|----|--7--|--1--|
5. |--1--|-----|--2--|-----|--3--|--4--|-----|--5--|----|--6--|-b7-|-----|--1--|
Aeolian b3, b6 & b7
1. |--1--|-----|--2--|-----|--3--|--4--|-----|--5--|----|--6--|----|--7--|--1--|
6. |--1--|-----|--2--|-b3-|------|--4--|-----|--5--|-b6-|----|-b7-|-----|--1--|
Locrian b2, b3, b5, b6 & b7
1. |--1--|-----|--2--|-----|--3--|--4--|-----|--5--|----|--6--|----|--7--|--1--|
7. |--1--|-b2-|------|-b3-|-----|--4--|-b5-|------|-b6-|-----|-b7-|----|--1--|
_______________________________________________________________
QuickView
(M=Major. P=Perfect. R=Root)
1. |--1--|-----|-M2-|-----|-M3-|-P4-|-----|-P5--|-----|-M6-|----|-M7-|--1--|
2. |-R1--|-----|--2--|-b3-|-----|--4--|-----|--5--|-----|--6--|-b7-|----|--1--|
3. |-R1--|-b2-|------|-b3-|-----|--4--|-----|--5--|-b6-|-----|-b7-|----|--1--|
4. |-R1--|----|--2--|-----|--3--|-----|-#4-|--5--|-----|--6--|-----|--7--|--1--|
5. |-R1--|-----|--2--|-----|--3--|--4--|----|--5--|-----|--6--|-b7-|-----|--1--|
6. |-R1--|-----|--2--|-b3-|-----|--4--|-----|--5--|-b6-|-----|-b7-|-----|--1--|
7. |-R1--|-b2-|------|-b3-|-----|--4--|-b5-|-----|-b6-|-----|-b7-|-----|--1--|
___
|--1--|-----|--
2--|-----|--
3--|--
4--|-----|--
5--|-----|--
6--|-----|--
7--|--1--|
|--
2--|-----|--3--|--4--|-----|--5--|-----|--6--|-----|--7--|--1--|-----|--2--|
|--
3--|--4--|-----|--5--|-----|--6--|-----|--7--|--1--|-----|--2--|-----|--3--|
|--
4--|-----|--5--|-----|--6--|-----|--7--|--1--|-----|--2--|-----|--3--|--4--|
|--
5--|-----|--6--|-----|--7--|--1--|-----|--2--|-----|--3--|--4--|-----|--5--|
|--
6--|-----|--7--|--1--|-----|--2--|-----|--3--|--4--|-----|--5--|-----|--6--|
|--
7--|--1--|-----|--2--|-----|--3--|--4--|-----|--5--|-----|--6--|-----|--7--|
In knowing this, one will know the identity of ALL the Modes since we know that the make up of a minor scale or chord has a b3.
(Arpeggios, Chord building and chord structure also derive from all this)
So:
Ionian.........(Maj) ............
1234567
Dorian.........(min) ........... 234567
1
Phrygian......(min) ........... 34567
12
Lydian.........(Maj) ........... 4567
123
Mixolydian....(Maj/Dom7) ... 567
1234
Aeolian........(min) ........... 67
12345
Locrian........(dim) ............7
123456
1. CMaj or Maj7th
2. Dmin
3. Emin
4. FMaj
5. GMaj or Dominant7th
6. Amin or relative minor
7. Bmin7b5 or diminished
(Western music utilizes Diminished, Augmented, Melodic & Harmonic minors)