There are lots of ways you can do this - but the simplest to understand are in terms of dynamics and rhythm.
So - a soloist may start a solo very sparsely and quietly - then it may be deemed "sensitive" - to play more quietly yourself and build with the soloist. So - you might want less volume for a quiet, reflective piano solo than for a tenor sax player who is blaring out at high intensity!!
As to rhythm - a soloist may suggest they are hearing a 2-feel rather than 4 to the bar - or they may suggest a double time feel - or they may take a song that starts with a Latin beat, into swing - they may even throw in bars in different time signatures - I've seen/heard this happen - moving to bars of 3/4 in a piece that was 4/4!
The possibilities are endless - that's what makes live Jazz so much fun!!
But basically it's just about
listening and being sensitive to what's going on, rather than ploughing your own furrow regardless!!