The early 1960s were a time of change in the jazz world. People like Miles Davis were beginning to investigate and incorporate other musical styles and formats and broadening the definition of what constituted jazz. There were the experiments with the music of other cultures and their integration into compositions, and this was followed by fusing jazz with elements of pop music, specifically funk.
Soloists were starting to lean toward more and more complex improvisations in their performances as they looked for newer and different ways to express the themes of a piece of music. Taking their cue from the postwar generation of players, like Charlie Parker, their playing became increasingly elaborate as the years went on.
At one point jazz was the preserve of orchestras that would sometimes approach symphony orchestras in size and make-up. But in the post World War two era more and more often you'd find smaller combinations of instruments ("combos"). These smaller groups were ideally suited for improvisation and solo work as fewer people meant easier communication between members while playing.
It's interesting to note that the groups today who are still experimenting with improvisation and solos are those with the smaller number of players. The Chicago Underground Trio, El' Zabar Kahil's Ethnic Heritage Ensemble, and his Ritual Trio continue to break new ground in improvisation techniques with specific focuses on rhythm and the use of electronics.
You can't talk about jazz and improvisation without talking about the influence of John Coltrane. Arguably, he was one of the most inspired and inspiring saxophone players in jazz if not ever, than at least during his lifetime. His recording career lasted only twelve years, and when he died in 1967, he was still at the peak of his skill level.
For some reason very little film of John Coltrane exists, although I'd say part of the reason would have been his unwillingness to tailor a performance to the needs of a television show. How many North American variety shows are going to have as guests a jazz band whose average song length was in the fifteen-minute range? Thankfully European television didn't seem to have the same hesitation and it's to recordings in Germany and Belgium that the Jazz Icons Series produced by Reelin' In The Years have turned for their wonderful DVD John Coltrane Live In '60, '61 & '65