Contributor: nmcsm

Modes are formed when a scale is used as a basis for creating other scales 
while remaining in the same key, or 'diatonic'. 
The name of the major scale is Ionian. When we start on the second note 
of the major scale and relate the rest of the notes to it, we get the second 
mode which is called Dorian. I'll chart it using the key of C.
C D E F G A B = Ionian
D E F G A B C = Dorian
E F G A B C D = Phrygian
F G A B C D E = Lydian
G A B C D E F = Mixolydian
A B C D E F G = Aeolian
B C D E F G A = Locrian
The mode names are used for every key and each is derived in the same 
manner as above. A bit like pig-latin.
Using intervals, this is what each mode represents:
Ionian = 1 2 3 4 5 6 7
Dorian - 1 2 b3 4 5 6 b7
Phrygian = 1 b2 b3 4 5 b6 b7
Lydian = 1 2 3 #4 5 6 7
Mixolydian = 1 2 3 4 5 6 b7
Aeolian = 1 2 b3 4 5 b6 b7
Locrian = 1 b2 b3 4 b5 b6 b7
When we list these by using intervals of thirds, we get the interval 
system for our chords and related extensions.
Ionian = 1 3 5 7 9 11 13 = MAJOR 7
Dorian = 1 b3 5 b7 9 11 13 = MINOR 7
Phrygian = 1 b3 5 b7 b9 11 b13 = MINOR 7
Lydian = 1 3 5 7 9 b11 13 = MAJOR 7
Mixolydian = 1 3 5 b7 9 11 13 = DOMINANT 7
Aeolian = 1 b3 5 b7 9 11 b13 = MINOR 7
Locrian = 1 b3 b5 b7 b9 11 b13 = HALF- DIMINISHED 7
One can notice the basic triads as the first three intervals when listed 
in thirds.
I hope this helps. 
      
         
If you don't read music think of it this way.
Have someone play a G chord or G bass note.
Now play DO RE ME FA SO LA TE DO over it starting on G.
That's G Ionian

Have someone play an Am chord or an A bass note.
PLAY the same notes, Do Re Me etc.
You've just played the 2nd mode, A DORIAN
The theory part of it is actually very simple.

Let a bass note ring or have someone else hold the chord. It's all about tone center.