A lot of these explanations are complicated for those of us who dont actually know much music theory. Here's a more simple rundown. Everyone knows that there are 7 notes in every scale(pop music). A chord is just any three pitches from a scale.

Now most chords are based on the major and natural minor(aeolian) scales. Now conventionally each chord is made up of: a root, the third note of the scale, and the 5th note of the scale. Other tones such as the 7th, 9th(2nd), 11th(4th), and 13th(6th) can be added on, however for our purposes they aren't important yet.

The 3rd and 5th and for basic jazz purposes the 7th determine most of the qualities of the chord. If the third is major it is a major chord. If the 5th is perfect(the 5th note of the maj scale) its still major, however move the 5th down 1/2 step it becomes diminished, and up 1/2 step it becomes augmented. The 7th determines whether a chord is dominant or not. A regular 7th (maj scale) is major while a flatted 7th is dominant.

Notes such as the 9th, 11th, and 13th can be added on to chords, extending their range, thereby making them known as extended chords. Flatting or raising these pitches makes the chord (and scale) altered, makaing the chords nown as altered chords. These chords are really only used in classical and jazz music.