Yes, I need to find time to create some documentation for that. But basically, it can be used for all sorts of things. I know of a user who wanted to log changes made to the copyright field of images. For me, I needed a way to log time spent on project management tasks on ipsguru. But theoretically, it could be used to log achievements to a user, or milestones to a topic, or moderation actions in a forum, or.... whatever you want to keep a log of.
In your instance, I'm not exactly sure what you mean by "overtime a member logs in", but the process is basically the same for any log you want to use.
Create the log in the Rules ACP under "Custom Logs" attached to whatever system entity (member, node, content) the log will be tracked to.
Add any additional log data fields you want to show in the log by adding "Log Arguments".
Through your own devised rules, simply add the action to add a log entry to the log in question whenever it is appropriate.
As an example:
On IPS Guru, I have a pages database for "tasks" that I use to track activity on specific tasks for custom projects. Through pages, I have a radio field that has two options for the task "In progress" and "Task Idle". I have enabled this database for collaborative use so that I can create tasks inside of collabs.
Via rules, I have added a custom integer data field to the "task" content type. So with rules, I set the current date/time timestamp when the task is updated to "in progress", and then calculate how much time was spent on it when the task is updated again to "task idle". I create a log for the task when the session is started, and when it is ended and have added a couple custom log arguments so that I can log the total time for the session, and an overall time for the task. Works pretty good for my needs.