characteristics of chords in scale can somebody explain

I have been reading that scales have chords and notes that define that scale sound like for instance I was reading that a aeolian characteristics chords are am dm f Idk this is all new to me can some explain this more
 
I will go out on a ledge and suggest that this http://www.billtroxler.com/f/25_Aeolian_Mode.pdf is what you are referring to. It is wrong.

1) Things I agree with in this document

Every scale has characteristic chords and notes - simple result of having a tendency for some notes that want to rise or fall.

C major (C Ionian) tones are C, F and B: F has a tendency to fall to e, B has a tendency to rise to C; chords are C, F and G - between them , they contain all of the notes of the scale.

2) Things I disagree with in this document

You do not build a minor chord above mode tone [sup]b[/sup]6 - that would be F minor in A aeolian (F-A[sup]b[/sup]-C) which contains a non mode tone A[sup]b[/sup]/G[sup]#[/sup] - no method for constructing the Aeolian that I can think of allows this particular construction (you might get away with it in the harmonic minor by fudging the use of the raised 7th and pretending it is a flat 1 instead

3) Why I disagree
In A natural minor (A aeolian) I would have thought that tones were A B and F and the chords were Am, Dm and G (again all notes of the scale appear in these three chords which is not true if you use F instead). Note that by using B and F as the other significant tones in the scale to construct a chord, we end up with Bdim (B-D-F) and G[sup]7[/sup] (G-B-D-F) as possible significant chords, further reinforcing the idea that G is the natural 3rd chord in the triumvirate of significant chords (yes we could have used Em, but it is not as solid a cadential force as G as in Em-Am vs G-Am; the second construction sounds more final and is in fact known as the Aeolian cadence).

In spite of many remonstrations against relying solely on wikipedia for some aspects of music theory, this article serves to provide a better overview as does this website
 
aeolian mode is just a fancy way of saying natural minor. Natural minor starting on the note 'A' has no sharps or flats. The characteristic chords of a scale are the ones that make it different from a major or minor scale.

A better example to understand this is mixolidian mode (I probably spelled that wrong) is the same as a major scale except for it has a lowered 7th. So mixolidian mode on the note 'C' is the same as C Major except for a Bb. The characteristic chords in mixolidian are any of the chords that use the Bb because that's what makes it different from major.
 
You have missed the crucial part - the chord built on the 5th degree of the mixolydian is chord v (minor)

Mixolydian
Roman numeralExample in CTones
ICC-E-G
iiDmD-F-A
iii[sup]b5[/sup]EdimE-G-B[sup]b[/sup]
IVFF-A-C
vGmG-B[sup]b[/sup]-D
viAmA-C-E
[sup]b[/sup]VIIB[sup]b[/sup]B[sup]b[/sup]-D-F
]

As with the Aeolian, the dominant function shifts from chord v to chord [sup]b[/sup]VII, however, this chord does not have a dom 7th built above, rather the dom 7 chord is itself chord I
 
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