"In game design the Mechanics-Dynamics-Aesthetics (MDA) framework is a tool used to analyze games. It formalizes the consumption of games by breaking them down into three components: Mechanics, Dynamics and Aesthetics." -Wikipedia
Game genres are a very loose grouping of games and recently the game making community
Mechanics are the base components of the game - its rules, every basic action the player can take in the game, the algorithms and data structures in the game engine etc.
Dynamics are the run-time behavior of the mechanics acting on player input and "cooperating" with other mechanics.
Aesthetics are the emotional responses evoked in the player.
There are many types of aesthetics, including but not limited to the following eight stated by Hunicke, LeBlanc and Zubek:
Sensation (Game as sense-pleasure): Player enjoys memorable audio-visual effects.
Fantasy (Game as make-believe): Imaginary world.
Narrative (Game as drama): A story that drives the player to keep coming back
Challenge (Game as obstacle course): Urge to master something. Boosts a game's replayability.
Fellowship (Game as social framework): A community where the player is an active part of it. Almost exclusive for multiplayer games.
Discovery (Game as uncharted territory): Urge to explore game world.
Expression (Game as self-discovery): Own creativity. For example, creating character resembling player's own avatar.
Submission (Game as pastime): Connection to the game, as a whole, despite of constraints.