One thing I notice when working with students who want to improve their sweep picking is that, very often, they're playing separate pick strokes instead of letting the pick brush through each string with no pause in the pick's progress.
This is most noticeable when trying to play or practice a sweep arpeggio at a slow tempo. Even guitarists who are able to get the sweeping motion happening just fine at quicker tempos often revert to picking each string individually as soon as they slow it down to try and synchronize the hands.
This is because the natural momentum of pushing or pulling the pick through the string is easier to feel when done at a medium or quick tempo. However, trying to do this in a slow and controlled manner can be a challenge, which leads us to the point of this lesson: the rest stroke.
In classical guitar, a rest stroke is where the finger plucks a string (say the D string) and comes to rest on the adjacent string (in this case, the A string). Obviously this term applies to fingerstyle upstrokes, but if we steal it and apply this to our use of a guitar pick, a down stroke on the A string would see your pick coming to a halt against the side of the D string. An upstroke is the reverse.
Simple, yes? Try it now. Pick any note on any string, and try pushing your pick through and letting it come to a stop against the neighboring string. You’ll see that if you wanted to go ahead and play the next string, all you have to do is allow the pick to push through the string it’s resting against. Now try linking together two pick strokes. Start by picking through