What the heck are modes?
They are a system of classifying music scales and are used in traditional Celtic music.

Below I will use chord names using letters but also their position on the scale with roman numerals, where Capital letters signify Major chords and lowercase signify minor chords.

I Ionian

Let us take a Major G scale, with its intervals of tone | tone | semi-tone | tone | tone | tone | semi-tone
the notes are: G — A — B C — D — E — F# 
The chords we play for a tune in G Major are
G Major — A minor — B minor C Major — D Major — E minor — F# diminished
Traditional music rarely, if ever, uses the 7 diminished chord and we will ignore it.

Using roman numerals:
I ii iii IV V vi 

As a 'Mode' we call it Ionian. Major = Ionian.
In Ionian, we use the I, IV, and V a lot, you will also hear the ii and vi . The iii minor (sometimes major) is less common but cool when you hear it.

II Dorian

If we take the same G scale, the same notes and the same intervals but start at the second note, A or II, we are now in Dorian Mode
and the notes are A — B C — D — E — F# G — A.
We could call this the Second Mode of the G scale, but we will call it A minor or A Dorian.
The melody may use a lot of A notes and almost always will end on an A note.
If you want to write the sheet music, you would use the G scale. If you used A Major you would have to use a flat-3 and a flat-7.
The chords we play for a tune in this mode (start counting from the A) are
In Dorian we use the i, VII a lot. You will also hear v and IV.

Trad music rarely uses the Mode that starts on the III, called Phyrgian.
Trad music rarely uses the Mode that starts on the IV, called Lydian.

V Myxilodian

If we take the same G scale but start at the fifth note, D or V, we are now in Myxilodian Mode
and the notes are D — E — F# G —A — B C — D.
We could call this the Fifth Mode of the G scale, but we call it D Myxilodian.
The melody may use a lot of D notes and almost always will end on an D note.
If you want to write the sheet music, you would still use the G scale. If you used D Major you would have to use a flat-7.
In Myxilodian we use the I and VII a lot. Also the v.

VI Aeolian

If we take the same G scale but start at the sixth note, E or VI, we are now in Aeolian Mode
and the notes are E — F# G —A — B C — D — E.
We could call this the Sixth Mode of the G scale, but we call it E minor or E Aeolian.
The melody may use a lot of E notes and almost always will end on an E note.
If you want to write the sheet music, you would still use the G scale. If you used E Major you would have to use a flat-3, flat-6 and flat-7.
In Aeolian we use the i and VII a lot but also any of III, iv, v, VI.

Trad music rarely uses the Mode that starts on the VII, called Locrian.

 CHORDS ON THIS PAGE

MODES based on G MAJOR

(Modes not common in Irish Trad: Phyrgian III, Lydian IV, Locrian VII)

IONIAN I on G (G Major)

G — A — B C — D — E — F# G

DORIAN II on G (A Minor) (A Dorian)

G — A — B C — D — E — F# G — A

MYXILODIAN V on G (D Mix)

G —A — B C — D — E — F# G —A — B C — D

AEOLIAN VI on G (E Minor) (E Aeolian)

G —A — B C — D — E — F# G —A — B C — D — E

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MODES based on D MAJOR

(Modes not common in Irish Trad: Phyrgian III, Lydian IV, Locrian VII)

IONIAN I on D (D Major)

D — E — F# G — A — B — C# D

DORIAN II on D (E Minor) (E Dorian)

D — E — F# G — A — B — C# D — E

MYXILODIAN V on D (A Mix)

D — E — F# G — A — B — C# D — E — F# G — A

AEOLIAN VI on D (B Minor) (B Aeolian)

D — E — F# G — A — B — C# D — E — F# G — A — B

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MODES based on C MAJOR

(Modes not common in Irish Trad: Phyrgian III, Lydian IV, Locrian VII)

IONIAN I on C (C Major)

C — D — E F — G — A — B C

DORIAN II on C (D Minor) (D Dorian)

C — D — E F — G — A — B C — D

AEOLIAN VI on C (A Minor) (A Aeolian)

C — D — E F — G — A — B C — D — E F — G — A

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MODES based on A MAJOR

(Modes not common in Irish Trad: Phyrgian III, Lydian IV, Locrian VII)

IONIAN I on A (A Major)

A — B — C# D — E — F# — G# A

DORIAN II on A (B Minor) (B Dorian)

A — B — C# D — E — F# — G# A — B

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MODES based on F MAJOR

(Modes not common in Irish Trad: Phyrgian III, Lydian IV, Locrian VII)

IONIAN I on F (F Major)

F — G — A Bb — C — D — E F

DORIAN II on F (G Minor) (G Dorian)

F — G — A Bb — C — D — E F — G

AEOLIAN VI on F (D Minor) (D Aeolian)

F — G — A Bb — C — D — E F — G — A Bb — C — D