Attention span is the time spent doing a single task. Broadly speaking it is the opposite of multitasking which is concerned with doing multiple task at once. Or, at least, dividing time between tasks. In my own experience which agree with the scientific studies, we humans are not built for multitasking. What multitasking does is split focus. It takes brain energy and time to orient or focus on a certain task. That means the more we switch between tasks the more energy and time is spent just for the brain to orient itself for the task at hand rather than doing the task itself. It implies more time is spent doing the whole task.
Increasing your attention span means focusing on a single task. With a higher attention span you can accomplish more than if you multitask. For instance, while writing this article I spent some trying to connect to the internet which wasn’t really helpful. If I had devoted whole of the time to this article and only later on tried to connect to the internet the total time consumed would be much lesser.
Increased attention span also means switching fewer times between task. If you’re running Facebook and reading newspaper at the same time. The most efficient way would be to either be done with Facebook and then start reading news or vice-versa. Switching to Facebook at the sound of notification while reading newspaper is more time consuming. Our mind wants to make lesser decisions. Increase attention span, make less decisions and be more productive.