A triad consists of three notes: a root, a third, and a fifth.
Let’s look at a major triad first. It’s composed of a root, a 3rd, and a 5th (1, 3, 5). Triads like this are built by stacking thirds on top of one another. The distance between 1 and 3 is a third, and the distance between 3 and 5 is a third. Note, however, that the third between 1 and 3 is a major third (1 2 3, two whole-steps), while the third between 3 and 5 is a minor third (3^4 5, one whole- and one half-step). Thus, we can think of the interval of a 5th as two stacked thirds: one minor, and one major.
In a major triad, the order of stacked thirds is (bottom) major, and (top) minor. But if we flip that order, we get a minor triad. A minor triad consists of 1, b3, and 5. The distance between 1 and b3 is a minor third (1 2^b3, one whole and one half-step) and the distance between b3 and 5 is a major third (3 4 5, two whole steps).
We also have diminished triads, which are formed by lowering the 5th note of a minor triad. Their formula is: 1, b3, b5.
We also have an augmented triad, which is formed by raising the 5th of a major triad: 1 3 #5.
Here’s what they sound like, in the order major, minor, diminished, augmented:
TL;DR: Triads are three note chords that consist of a root, third, and fifth. They can be major, minor, diminished or augmented. The formulas are: major: 1 3 5; minor: 1 b3 5; diminished: 1 b3 b5; augmented: 1 3 #5.