Just what it says. You cannot perform any takedowns, kill anyone, shoot them with a choke arrow - anything that leaves them dead or unconscious. Reloading a checkpoint after you kill someone or knock them out is allowed, assuming your checkpoint is before the attack.
Well, almost what it says. There is a forced takedown in the Prologue. You can't avoid it, the game will actually prompt you to take down a guard, and you have to do it to proceed. This one doesn't count.
This achievement will come naturally if you use the recommended difficulty settings for:
The Something to Prove achievement in THIEF worth 554 pointsFinish the game with a custom difficulty of 700 points or more
...or if you just turn on the "No Kills or Knockouts" in the custom difficulty settings when starting your game. With this setting on, if you kill someone or knock them out, the game immediately fails you and you must reload - so if you can finish with it on, you'll get this achievement.