Unfortunately when starting, a pageful of code like the above can be daunting. However it is a very good example of how to use local storage.
Lines 1-4 - Retrieve High score from local storage
Lines 5-6 - Simulate game increasing your score
Lines 7-9 - Save High score to local storage
Lines 10-12 - Not applicaple to the query
Local storage is very useful and imo even more so when combined with a dictionary object to avoid racing issues for multiple variables.