) - A chord is a set of notes, usually played at the same time, that form a particular harmonic
relationship with each other. The most basic chord is the triad
Chords (in western music) are usually built by stacking thirds. This means that from the root of the chord, you add minor or major thirds (usually, depending on the scale). The triad is generally the root (first), third and fifth of a scale. So if you have C major - the notes of the scale are C D E F G A B, and to build a major triad you take the root (C) and add the third (E), and the fifth (G), which is also a third above E. For a more in depth discussion - read triad.
The triad can be extended by adding more thirds on top. For instance, if you take a C major triad (C, E, G) and add a B (a third above G), you have a major 7th chord (Cmaj7 or CM7), so called because the notes come from the C major scale. Similarly, if you take the A minor triad (A C E), and add a G, you get a minor 7th chord (Am7 or A-7).
Extensions to all the seventh chord can be created by adding more thirds. For example, adding a B to the above mentioned Am7 chord yields Am9 (B being the ninth of A). Adding a further D (a third above B) yields Am11, and adding an Fon top of that yields Am13.
The simplest way to see this is by looking at the A minor (natural) scale, and writing it in two octaves. Then thirds are seen as 'every other note':
A B C D E F G A B C D E F G. Thus, using any scale, you can easily build a triad, a seventh chord, and add tensions. Of course, not all tensions are available.
See also triad, 7th chord, Guide to chord formation.