You can build a chord on each of the scale degrees. The chord will have the same name and Roman numeral as the note it's based on. The notes in the chord are spaced a third apart (That's every other letter name, for the intervallically challenged out there). The four notes in each chord are designated the Root, Third, Fifth and Seventh. Here's how they lay out, with the chord names included:
Look carefully. All the notes in all the chords come from the C major scale. A tune in the key of C can have any or all of these chords.
Chords have two aspects: quality and function. Function describes what the chord does in the structure of a tune. But be aware that one chord can function in several ways in more than one key. For example, in the above diagram, Emi7 is the iii chord in the key of C. It can also be the ii chord in D or the vi chord in G. So don't become confused when you see the same chord in another key.
Quality describes the sound of the chord. The primary chord quality is either major or minor. It's determined by the third of the chord. In the above example, we see Cma7, Fma7 and G7. The thirds of each of those chords are two whole steps above the roots. That is the indicator that they are Major chord types. In Dmi7, Emi7 and Ami7, the thirds are a step and a half above the roots. Those are Minor chord types. I'm omitting Bmi7(b5) for now as it is a special chord.
That, grasshopper, is why we have upper and lower case Roman numerals! The arrangements of major and minor chords in a Major key is set in stone. I is always major. ii is always minor. And so on. The Roman numerals help to illustrate this. Need help playing these chords? Check out the jazz guitar chords lesson.