Why does multi-tasking lead to a drop in productivity?

More than one task splits the brain. Whenever you need to pay attention, an area toward the front of the brain called the prefrontal cortex springs to action. This area, which spans the left and right sides of the brain, is part of the brain’s motivational system. It helps to focus your attention on a goal and coordinates messages with other brain systems to carry out the task. While the right and left sides of the prefrontal cortex work together when focused on a single task, the sides work independently when people attempt to perform two tasks at once.

Source: http://www.brainfacts.org/Sensing-Thinking-Behaving/Awareness-and-Attention/Articles/2013/The-Multitasking-Mind