First, focusing on one task requires planning, believe it or not. Starting your day without a plan is just asking for distraction and inefficiency. When you sit down in the morning to plan out your to-do list it forces you to prioritize and consider what tasks will have the highest impact on your work. This prevents you from getting lost in the never-ending weeds of seemingly urgent, yet unimportant work. Employees who do this are the ones who move the needle on important projects and catch the attention of superiors as big contributors.
Next, intentionally focusing on one task at a time has been proven the most efficient way to move through the work day. It lowers feelings of stress, frustration, and perceived effort. Working through your to-do list one task at a time is an effective way to become a happier, more productive employee. People who are less emotionally or physically drained are able to accomplish more than those who are, on average. There are rare situations where people genuinely thrive under pressure. In most cases, trying to focus on too many things at once leads to people feeling overwhelmed, which is not where most people want to be.
Along the road to increasing productivity by focusing on one task a time there are bound to be mistakes. One key of the most productive people is being able to bounce back from failures. They do this by first recognizing that they have gotten off-track, quickly determining how to get back on-track, and then setting up whatever safeguards they can in the future to prevent that specific thing from causing problems again in the future. Emails are pointed out as the biggest offender when it comes to distractions, so putting safeguards in place to help with that is probably a good idea on the road to being the most productive you can be.