Multi-tasking is....
...a myth. Numerous studies have shown that multi-tasking results in poorer work performance by most measures (lower productivity, more errors, less job satisfaction, etc.) than focusing on a task and completing it. Many of these studies indicate that the human brain does not perform well at multi-tasking. A study from 2008 estimates that multi-tasking could cost the U.S. economy $650 billion annually in lost productivity.
"Multi-tasking" is a term that attempts to make a virtue of being expected to do more than can possibly be done in the time available. It places the burden for poor management decisions (not hiring sufficient staff, poor planning, new initiatives launched before the people charged with them have been able to complete the previous initiatives) on the employees stuck with the mandate to multi-task. It may be today's reality, but it's a bad business strategy.