I saw this image online, and it while does a great job of explaining triads to anyone who already knows what it means, but if you don't, well, what *does* it mean? Well, here's a brief explanation I came up with. It should make sense, but if anything's unclear please let me know in the comments

http://i.imgur.com/9nfoeBO.jpg

(and to be clear, this is not my image - author unknown, or I'd credit them. All text here is, however, mine)

A triad chord consists of three notes, but you can also think of that as a start note ('root'), and then two other notes some distance away. You start on one note, move to another, then move to a third. Those movements are called intervals, and when dealing with triads, will be either 3 or 4 semitones (notes). This gives us two options for each:

0, or m, or 3 semitones, or a minor third interval, or an empty oreo (these are all the same thing)
1, or M, or 4 semitones, or a major third interval, or a full oreo (these are all the same thing)

Given that our possible combinations for two digits are:

00
01
10
11

To put that in m/M notation, that is:

mm = diminished triad
mM = minor triad
Mm = major triad
MM = augmented triad

Now, we only have two digits here, so how are these triads? That's because we're dealing with intervals, and an interval goes from somewhere to somewhere, so the third part, the root, is already implied.

If that's a bit too abstract, here's an example. Remember:

m = 3 semitones (aka up 3 notes)
M = 4 semitones (aka up 4 notes)

Pick a root, any root. Let's say... F

Now pick a chord type - let's say major, which is Mm so our formula is going to be

F, M, m
which is
F, 4 semitones up, 3 semitones further up
which gives us:
F, A C, which is in fact F major

F minor would be:
F, m, M
so:
F, 3 semitones up, 4 semitones further up
giving:
F, G#, C, which is F minor

Try this for any chord. There you go, boom. music theory.

This also explains why when you're playing on only white keys (C major/ A minor) the triad starting on B is the odd one out in terms of sound. It's diminished, when all the others are major or minor.

So there you have it. Music theory with cookies. Happy musicmaking!

(Edited for minor typos)