When it comes to productivity it's easy to obsess about the tasks on our to-do lists and fail to identify what the successful outcome (i.e. the end result we aspire to reach) is. We may even mistake a milestone for the destination.
Writing a book is a great accomplishment, but is that the end of the road? Or should you work on publishing and then promoting the book? The end result you aspire to reach with the book would likely be to have in the hands of as many people as possible. Writing it and not distributing it is not following through to the end goal.
Follow-up is part of the process of ensuring you follow through with your goals, but it involves other people and external factors you're dependent on to reach your ultimate aim. In many situations the people you deal with might not be invested in your goal as you are. It may not be a shared goal (e.g. a printing house may not care if printing is delayed while they work on other client projects) or they are not invested as much as you are (e.g. a business owner vs disengaged staff).
To follow-up means to express your commitment towards your goals, even if they are dependent on other people. You don't want to blame others for your failures. You want to overcome the obstacles standing in your way.
I often struggle with follow-up because I'm too engrossed in my own work and "out of sight, out of mind." This is a reminder for me to ensure that I see my projects through, including follow-up and changing course, if the path I've chosen is not the path that takes me to the goal I want.