What is an activity log?
An activity log is a daily or even hourly summary of all your work accomplishments. It is the flip side of a journal. Instead of being forward looking, it is backward looking. It is done.txt to your todo.txt. (In fact, if you use todo.txt like I do, done.txt is your activity log, albeit at the most atomic level.)
Maintaining an activity log is simple. At the end of the day, spend 5 minutes to sum up what you've done and where you stand. Think about it like updating your journal.
An activity log can be useful to sum up your work for the day, and to read in the morning (as you are updating your journal) to pick things up where you left them. This summing up is most useful if you don't keep a task list for some reason.