Basically when members of the group swapping four bar phrases. The idea of trading fours in today's contemporary American styles goes way back in our musical history. We can trace it's origins back towards the communicative form of call and response, an integral part of many of our early religious ceremonies. What basically occurs in this format is a stated "call" by the leader of the group followed by a response from the listeners. Powerful in it's abilty to get everyone involved, we modernists evolve the call and response concept into an exciting, improvised performance event.
Often found in jazz, trading fours happens in a number of setings. In larger groups, as say in a big band, we often hear a trading of fours between the various sections of the band. In smaller group settings, especially from the Bop era forward, the trading of fours is often between each of the voices within the group. Today, when players trade fours, it usually occurs towards the end of an musical arrangement.
For example, let's say that a jazz quintet, pianp, bass, drums and two horns, is performing a 12 bar blues song. After the melody has been played down twice, each of the players in the group will improvise a solo over the form of the tune. At the close of the arrangement is often where the trading of fours will occur. Using the 12 bar form, the first of the soloists will play just four bars, the next soloist will take the next four etc., following the form of the tune. After trading a bit, the original melody is then restated to close out the piece.
Variations. Depending on the level of expertise of the players within the group, a couple of common combinations often occur.
That the trading of four bars will occur between just two of the solo voices. Here we often hear a bit of call and response or conversation between the players. One voice takes four bars, then immediately the second voice picks up the thread ogf the line for four bars, then back to the first voice. In this setting, players will often mimic each other, play the exact line back, or try to increase then energy level before handing back the line. Very exciting to perform as well as listen to.
Another very common idea in the above format is to trade fours with the drummer. In this setting, each of the solo voices improvises four bars usually with the backing of all the players, then the group stops while the drummer responds with a four bar idea alone. Then the group comes back for four bars, then back to the drums for four. If you've got a good drummer in your group, this is a very fun way to open things up a bit and create some excitement.
Of course, any group of any number of players can trade musical ideas in this format. Must it be four bars? Nope, any amount of bars will work. Experienced players often play eights, then fours, then two's and then one's before the restatement of the melody. Needless to say, this type of trading can heat things up in a hurry ... or create some serious trainwrecks!