The greek word "Diatonikos" means playing Natural Tones (notes) only; on the keyboard that`ll be the white keys.
So a "C major Scale" or "C Ionian" is diatonic.
and so is the "A natural minor" or "A aeolian".

The fallowing modes and scales are Diatonic as well:
D dorian
E Phrygian
F Lydian
G Mixolidian
A aeolian
B Locrian

"G Major pentatonic" [G,A,B,D,E]
"A minor pentatonic" [A,C,D,E,G]
"E minor pentatonic" [E,G,A,B,D]

Any chord that contains natural notes only is said to be a Diatonic chord:
G=[G,B,D] is a diatonic major triad.
Em=[E,G,B] is a diatonic minor triad.
Dm7=[D,F,A,C] is a diatonic minor seventh chord.

Now compare these two Major scales:
1) {C,D,E,F,G,A,B}
2) {G,A,B,C,D,E,F#}
The first is a diatonic scale. The second, however, is not; because it has the "F#" in it.

Now compare these two minor chords:
1) [A,C,E]
2) [C,Eb,G]

The first is a Diatonic chord. The second one is not, because it contains an "Eb" in it.

The second mode of the "G major Scale" Is "A dorian"
A dorian=[A,B,C,D,E,F#,G]
and is not a diatonic mode, because of the "F#"

I hope that helps.