Accolades are given to you for performing specific acts in the game - like killing enemies with specific weapons, exploring, playing in Co-op etc. Every accolade has 5 levels. Once you have received enough accolades your Accolade level goes up by 1 and you get some rewards, mostly cosmetics and emotes for Co-op. I'm at accolade level 9 now at character level 21 for reference. Try to switch out your weaponry often to boost this a bit, every weapon type has separat accolades. You can track everything from the Accolade-menu ingame.
*Edit* Reached Accolade level 10 at character level 23