Centurion Difficulty is your basic Hard Mode. Enemies hit for more damage and you get less rewards for your executions (IE: executions don't return as much health if you have the health bonus selected).
UNCONFIRMED - It feels like enemies take more hits to become executable/killed, but I don't know for sure.
My best advice is to beat the game on Soldier (Normal) first and really get used to the combat system. Also, if you plan on beating the game on Legendary you MUST memorize the animations of attacks that cannot be Blocked. In Legendary the enemies will not glow red when you need to Roll to dodge them.
The important thing to note is that difficulty achievements are stackable, so you can complete the game on Legendary and get credit for this achievement.