People often want to know what variety of a say turnips you planted. Where you bought them. Whether they are organic seed stock. Who certified them organic. If you keep track of that stuff you can tell them. If you are thinking about entering some of your veggies in the State Fair you will need this information as well. There are literally hundreds of varieties (cultivars) of lettuce. There are hundreds of cultivars of carrots. If you don't write down the ones you plant and where you plant them you will have no idea what variety works well under specific conditions and which ones don't. Each year I record more information because I find I need more information each time I plant. What did I do when, where, and how. If you don't have a diary you will not be able to answer these questions.
Problems with pests in the garden should be recorded in the diary as well. More important than the pests is the remedy you used and how successful the remedy was. The information would be especially valuable the next time you encounter the difficulty.
I use a calendar to keep track of temperatures and rainfall. I can jot down a quick note on a the calendar about something that struck me that day. If I wait to write it down later I will forget it. I now know that something like writing this blog helps me to remember what needs to be done and when. Obviously during 2017 I didn't do a very good job of writing and I'm sure I am kicking myself in 2018 because I was so lazy. You can do something as simple as tacking up a piece of paper in the garden shed and record you information there.
The diary should start your planning. Writing down your plan will help you execute it. It will help you see the steps required to get from preparation, to planting, to harvest. If you don't write it down lots of information goes away. I am sometimes asked, "what's the worst thing about Don"? My reply is usually, "if I don't write it down I forget it".
A diary is an indispensable document for the gardener. Writing a blog about gardening or a specific garden is also a great way to keep a diary but it's not detailed enough usually.