This is a fairly simple time management principle, but it's critical that you pay attention to it.
There are a number of things in your life that rely on another person taking action for you to move ahead. You need a system for following up on these things because you can't expect your brain to automatically track it and follow up at the right time. Also, unless you only deal with incredibly reliable people (a very low percentage of the population!) you can't expect the other person to do exactly what they said they would do without giving them a friendly reminder.
Some examples could be: you loaned a book to a friend and you're waiting for them to get it back to you, you called the travel agent and they are going to call you back regarding a flight, you asked your co-worker to get something accomplished which you need for your work and so on.
It's critical to keep track of these things by writing them down. If you rely on your memory and brain, you will let some things fall through the cracks. Most brains are just not designed to remember and keep track of all this sort of information - it's so much easier and more effective to write it down. After you have written it down you also need a system to consistently review your list and make sure that you are following up on what you need to follow up on.
So how do you make sure that you follow up with people at the right time? If you know it is a specific date in the future that you need to remember to follow up with this person, write down in your diary on that day to follow up with them. On the other hand, if it's not a specific day then you can write it down in a list and then make sure you review that list probably once each week to see if there is anything that you have forgotten to follow up on. Out of the items on the list that you are “following up” on, there are probably some that you have resolved but there might be a few that you have forgotten about.