I'll make the same distinction that some others have made:
Sometimes I'll "listen" to music while doing other things like surfing the web or taking a shower. For me, that is background music I play because the main activity isn't occupying my whole mind; the music makes the activity go faster and seem more pleasant. Usually that means a CD or computer-sourced music.
But sometimes I just LISTEN to music. Then I do nothing else but listen, often with my eyes closed. Usually that music is coming off a spinning LP, or sometimes tape.
The former type can be anything remotely suitable, sometimes what is chosen by a deejay. The latter is always carefully chosen to suit my mood.
Oh, and anyone who thinks multitasking is a talent is either very ignorant, really deluding themselves, or making a joke (Of course, I think it was the latter, in this thread). Multitasking is the easy way out, produces (usually) worse results in each task, and requires less intelligence. It may even be a sign of a mental disorder such as ADHD. If the multitasking involves three challenging tasks, like riding a unicycle while balancing a kitchen pot by the handle on your nose while also juggling slippery live fish, then it might be a good form of training and a real accomplishment. But if the three tasks are no more challenging than watching a computer screen, it's nothing to be proud of!