There's a couple of ways to track how many lessons your child has completed.
If you visit "My Stats" on the About Me page you will see the entire record since they first started ABCmouse.
If you're looking for a little more insight on those completes lessons, you might want to visit the Parent Section. As you enter this page you will get a Newsfeed on the right side that will list out the time and title of the lessons completed for all or individual profiles.
Finally, the last place you can look is the Progress Tracker feature, also found in your Parent Section!
The Progress Tracker allows you to see the amount of time your child has spent playing ABCmouse; this can be filtered into weekly or monthly intervals. You also have access to the number of activities completed by your child. The data can be displayed with the Overview number of activities, usage by subject, or time spent per category and then filtered into weekly, monthly, or overall time on the site