Recording the sets, reps and weight is enough for a lot of people.
If you want to make the most out of this tool you can also use your training log to write out the following things:
Use it to set goals for the week. Progression happens via knowing what you did last week and doing it a bit better this week. Having a clear record of your training history means that you are always striving to progress and improve.
Note the important out-of-gym stuff. I keep brief notes each day/workout on the previous night's sleep and how well I ate. The previous night's sleep, in my case, is easily the most determining factor of how well I perform in the gym that day. Keeping track of how well I sleep means that I am more focused on insuring a good night of sleep each day.
Write notes and thoughts. Your workout log can be just as much a training journal where you jot down thoughts on your workouts. Writing out my workouts has become part of the workout ritual/habit. I make notes of things that felt good, felt bad (handy for warding off injury), and thoughts on the next day of training.
Share it with your coach or trainer. If you work under the guidance of a trainer it can be helpful for him or her to go over your workout log from time to time. Better educating your trainer on how you respond to specific workouts and training regimens will only help them better plan your future training.