I've heard the term "session musician" in a few books I've read or videos I've seen, in context like, "You probably wouldn't need to really learn B major deeply unless you're a session musician." It seems counter-intuitive to me - why wouldn't I want to strive for fluency playing in any key (I play piano, if that helps).
A session musician is a "gun for hire". They get hired to put down parts in different studio sessions, hence the name. It is required to quickly learn parts in a lot of different styles and settings; they are likely to encounter more different tunes than most other musicians.
In your quote, B major is considered unusual enough that the casual player, or even professional player in a certain style, does not need to be fluent in it. The session musician is expected to be up for whatever is thrown at him/her though.
I am a session musician, and producer. Session musicians are called to come to the studio and play on a music track for songs, demos, advertising music, film scores, etc. There is little or no practice or rehearsal time. Imagine the piano player who was called to play on the music for Bugs Bunny cartoons (with the orchestra, of course). He or she had to be able to sight read flawlessly at high speeds, and who knows what the music could be: plunking, boogie-woogie, classical, special musical effects . . .
I can read regular music in any clef, chord charts, and Nashville number system charts. You must be able to contribute to the music and deliver-not only with no mistakes, but with lots of feel and precision. I have played in sessions next to some of the great session players: guys who have played on #1 rock and country hits, big name jazz players, and Orchestral masters. It's a blast if you can take the pressure (I just see it as a fun challenge, not pressure) You must also be able to take direction and criticism and change styles quickly. Your gear must be in top shape.
Practice, listen to lots of music, and be ready! It's a blast. But because time is money to the producer, they will not call you back if you didn't perform well, with no excuses or stories, if you're not on time, or if you are difficult when they ask you to do something you think is moronic, or can't be done. It's not for everybody, but it's a lot of fun.
Tommy Tedesco, a very famous guitar player in LA said that session playing is 95% boredom and 5% sheer terror. He had to bring guitars, banjo, bouzouki, ukeleles, zithers, etc., because he didn't know what the job would be. You've heard him play on many many TV show themes, records, movies, etc.
That term has a lot of definition but basically, they're individual musicians who are contracted to play to a live gig or more commonly, a recording session. Producers, song-writers, soloists usually hire individual musicians for their needs, instead of a whole band.
Naturally, they have to be fluent, proficient and versatile if they want to be sessionists for long because they have a big range of clients; hiphop producers, country singers, rock bands, even film scorers. They also have to be able to sight-read and play by ear.
I agree that you should strive for fluency in any aspect of your instrument. But not every musician need deep musical theory knowledge to be able to play.