Energy randomisation (also called speed randomisation) is a game mechanic designed to add unpredictability to monster behavior, and to nerf pillar dancing. Monsters normally get to take a number of monster turns per player turn based on their speed: fast monsters act more often, slow act less. However, the game will occasionally and randomly give enemies 90% or 110% of the amount of time they should get, allowing you to occasionally gain a tile of distance between yourself and an equal speed pursuer, or to allow a pursuing enemy to occasionally attack you as you flee.
A monster can only get energy randomisation when one of its actions is a move.
The name "energy randomisation" comes from the fact that the manner in which monsters move is described as "energy" in Crawl's code, with DEFAULT_ENERGY referring to moving at the same speed as any other action the monster takes. Hence, energy randomisation is inflicting randomness into this "energy". It can also be referred to as "speed randomisation", although this may falsely imply that the randomisation applies to all actions, not just movement.