Engagement is the quality and quantity of attention that a game gets from a player. Modern game executives often think in terms of engagement rather than gameplay because it is a more definable and measurable quantity.
Engagement has a polarity: positive engagement (enchantment) or negative engagement (retention). Positive engagement comes from creating a fascinating or entangling (or both) game world and is more likely to build lasting relationships with players over the long term. Negative engagement comes from creating a nagging but mildly diverting game which relies on repeat visits and repetitive tasks. Negative engagement is easier to model, but ultimately of lower value.
The quality of engagement is best described by the Engagement Hierarchy. The quantity of engagement is measured in terms of how many hours players play the game and how often they return. Beyond a certain threshold it shows that a game has traction.