Starring a strategy makes it a favorite for that account and allows you to access it directly from the optimizations drop-down menu, meaning you don't need to go to the Rule Engine page to run it anymore. It is a good idea to star/favorite frequently used strategy.
Global Strategies allow you to create a strategy to be used across all your accounts, without having to replicate it manually in each one. It is like building your own custom optimization and for ease of use, it can be accessed directly from Optimizations -> Rule Engine. Global Strategies can also be included in Custom Workouts.
You can convert a strategy to a global strategy on the strategy pages, by modifying it through the right-side actions, and use the same action button to revert it back to an account-specific strategy as well.
You can check some frequently asked questions here.