This is a term which is used a lot, especially in academic circles, when it comes to teaching.
Basically it seems to refer to how a specific pursuit like studying a musical instrument can relate to your actual life. At first that seemed a little irrelevant, but I've begun to realise recently how much studying music has impacted my life, and the lives of all my colleagues.
Its about your 'voice'. I've found that I behave very similarly on stage as I do off stage. Especially when I'm called on to improvise, such as in jazz. When you are trying to be a brilliant musician, you end up asking the same questions that you use to define personality types. For example, 'do I say too much?', or 'do I not contribute enough to a situation?'. 'Do I listen when other people are contributing, or do I just wait for my turn to come around again?'. Whether you're playing pop, soul, swing and especially jazz and orchestral music, there's a balance you have to strike between saying something, but not obliterating everyone else. Which is just like having a chat. Your musicianship and your attitude to music reveal alot about yourself.
Socialising is a big part of being a musician anyway. Whether it's an 18 piece big band, or one teacher and one student, you have to learn to negotiate, to communicate complex ideas, and to listen to other people's complex ideas. You are also a salesman: from your clothes to your handshake, you have to convince someone that you are professional and should be taken seriously.
So as a musician, you're part of a deep-thinking group of people. Musicians have to reflect on themselves and try to improve for next time, they have to have a sense of confidence without arrogance, and most importantly, they have to acknowledge and appreciate beauty and soul. Whether its a Chopin nocturne or a big disco back beat.
And finally, the best transferable skill is appreciating the craft. From symphonies to the twelve bar blues, good music can be loved by all people. But if you know a little bit about how something is put together and why, and you can maybe create your own version with other people, well its better than.... anything!