Commendations are the milestones you pass for doing activities for the 3 trade companies.
Each company has 12 categories and 5 levels in each making a total of 60 commendations for each company. The actual activities required are:-
Sailing on company business.
Multiple categories for handing in rewards (each level of treasure chest / skull / animal).
A couple of company specific categories (e.g. attacking skull forts for Order of Souls).
You just need any 10 commendations. If you spread your time between the different companies and earn the first level commendations in lots of different categories you should get this in no time.