Notice how I picked up on the rhythmic phrase that the pianist played at the end of his solo and used it as the basis for mine (listen around :17)? Passing ideas between soloists like this weaves the music into a more cohesive whole. This technique is a great one because strengthening the connection between solos benefits both the musicians on the bandstand and the audience.
You see? They love it!
Musicians will feel that you are listening and responding to what they are actually doing, not just operating in your own mental space. This in turn will give them the confidence to take more chances with the music and generate lots of positive energy.
In my experience, audiences also love this kind of interaction on the bandstand. Jazz is not popular music anymore, and often times audiences will not have a lot of experience listening to it, especially not live. Passing ideas like this is a way of bringing your audience into the performance by making the connection between solos as clear as possible.
Dont Forget About "Yes, And"
For this kind of interaction to work you need to remember the principle of
discussed in an earlier post. The basic gist is, when you are passing ideas don't just parrot back whatever the last person played, add something of your own to it. In the clip above I did this by adding my own idea at the end of my phrase.