The comments to the above clip point out that Ben Webster clearly is crying after Teddy Wilson’s piano solo. The explanation provided — there is no way to verify it, of course — is that Johnny Hodges, with whom Webster had played in Duke Ellington’s band, had just passed away.
Everything Webster played was beautiful. One story that I read in more than one place is that when Webster began rehearsing a song that had lyrics he would learn those words in order to play them on his sax.
Here is Flying Home — the tune I originally was going to embed until Old Folks popped up — The Brute, C-Jam Blues, Chelsea Bridge and Over the Rainbow. The New Yorker did a piece on Webster about ten years ago. Basic biographical information and discographies can be found on many sites dedicated to Webster, including these two.
A special acknowledgement is due to the JazzVideoGuy, who initially posted a lot of these clips and others that I use. He does a terrific job of, well, doing what his name says.