Studies have shown that having an unfinished task on your desk really does impact your ability to focus. Not having tied up the loose ends has a way of playing on your mind. Whether the task was abandoned because you were interrupted, you're lacking vital information or have been assigned something which takes priority, that unfinished business will make it harder to concentrate.
While you're trying to focus on your new task, the incomplete one will linger in the back of your mind. You may still be trying to work out how you'll proceed with it, searching for solutions. By still having it in the background, your cognitive energy is split between the two and you'll struggle to concentrate on the job in hand.
That means that while we may think multitasking is more efficient, it's really not. We're programmed to seek closure to things. Even people without a perfectionist streak will struggle to forget a task left unfinished, because they know they will have to return to it at some point. Until it's resolved, you don't have all the brain power you need to make a good job of your new project.
If you absolutely have to abandon one task for another, one of the easiest ways you can free up some headspace is by making notes on the next steps you have to take with it. That could mean bullet-pointing what more needs doing, so you have a clear plan of action in mind. It's not ideal, but it's one way of reassuring yourself that it will get done and will soon be off your desk and off your mind.
An unfinished task lingers in the back of your mind
Your brainpower is split between two tasks
Multitasking is seldom efficient
Try to make a plan for the unfinished job