People often associate sweep picking with arpeggios. But it is important to realize that arpeggios are simply chords whose notes are played individually. Sweep picking is simply a technique for playing arpeggios (Jazz trumpet players play arpeggios but you can be sure they are not sweep picking them - maybe sweep blowing?)
The exercises in this lesson go over a particular type of arpeggio called the triad. If you want to learn a little about the theory behind triads, then check out the Diatonic Scale section. I give a brief overview there. Basically, if we were to examine all 7 diatonic scale modes and form triads by taking the 1st, 3rd, and 5th notes of each scale, we would find that there are only 3 unique triads. These are the Major, Minor, and Diminished triads. I have indicated them in 3, 4, and 5 string form and you should become comfortable with them in that order.
Make sure that when you play the exercises you don't let the notes bleed into one another. I recommend that once you get up to speed, you record yourself and then use a program like Cool Edit Pro to slow down the recording and confirm that you are indeed playing all the notes. It is easy to muffle them (i.e. they get lost in the sweeping motion) and evaluating recordings will help you assess where you stand.
This exercise shows you how to play a Minor triad arpeggio across 3 strings using sweep picking. The arpeggio is a D Minor triad. Note how vastly different it sounds from the Major triad. Whereas the Major triad is bright and happy sounding, the Minor triad sounds darker. In any given key, there are 3 Minor triads you can play. They go along with the 2nd, 3rd, and 6th notes of the Major scale (i.e. with the Dorian, Phrygian, and Minor modes). In the key of G, for example, you could play an A Minor, B Minor, and E Minor triad arpeggio.