Trading fours is a jazz performance convention: after the head and the main solos, the band takes turns soloing in four-bar increments. The horn plays four bars, the drummer plays four bars, the horn plays four, the drummer plays four. (You also get "trading eights" and "trading twos" — the duration changes, the principle doesn't.) It's a jazz-specific structural game built into the form.
Why four bars? Because the standard jazz form (the 32-bar AABA standard, the 12-bar blues) is built out of four-bar phrases, and trading fours respects that phrasing. Each four-bar trade is one phrase of the form. The soloing drummer is filling in for the horn during one of the form's natural phrases, then handing it back.
The Practice Format
You can't really practise trading fours alone with a metronome — there's no horn to trade with. The practical workaround used in this lesson is the solo-bar template: comp for three bars, solo for one bar, comp for three bars, solo for one bar. The single solo bar is a stand-in for the band's four-bar phrase, scaled down for solo practice. Once that's automatic, you scale up — comp for four bars, then solo for four bars (Exercise 2).
Motivic Development
The hardest thing about a four-bar solo is making it sound like a phrase, not a random fill. The traditional solution is motivic development: pick a small rhythmic idea (a "motive"), play it in bar 1, vary it slightly in bar 2, vary it again in bar 3, resolve it in bar 4. The idea is recognisable across all four bars because all four bars are versions of the same shape. Exercise 3 demonstrates this with a single 16th-note triplet motive.