Training can be confusing and it can be hard to stick with a plan. With a training diary you get a better overview of your training and it will be easier to plan.
It can often be hard to see any progress from day to day which can make your motivation drop, but with a training diary you can easily see the progress over a longer period of time.
By being able to view and review your training it becomes easier to see patterns and that enables you to tweak your training to reach your goals.
Some days you will feel down, it feels like you haven't done anything lately. Having a training diary gives you the opportunity to look back and get visual confirmation that you actually have done something.
Being accountable for the logging of your training makes it harder to skip a day. Sharing it with others online makes you even more accountable.
Weather you feel like it or not, you can be a role model for someone. By keeping and sharing your training diary, you could inspire and motivate someone else to start or stick with their training.