Fighting styles can be modified and advanced to another level. Some features will specifically state you should advance a Fighting Style, but when you are given the option to choose an additional Fighting Style by a feature (such as a Fighter’s Expanded Fighting Style feature) you can choose to advance a Fighting Style instead.
When you advance a Fighting Style it always advances in stages in order of Base (its base effects), to Lesser, then to Greater.
Not all Fighting Styles have all of these stages.