What are game mechanics?
Conceptually I think of the mechanics of the game as how it's played but the definition is a little fuzzy. I don't think rules and mechanics are the same - although I think they're related. Help me sort this out in my head.
There is a fantastic article on this topic by Miguel Sicart called Defining Game Mechanics, it is mostly related to Video Games, but the the same definitions can broadly be applied to Board Games as well.
Essentially Game Mechanics are actions that modify the game state, and it is this modification of the game state that results in gameplay.
While Game Mechanics can, and should, be defined by rules, they are not themselves rules.
In a more colloquial form, if you're changing anything in the game, whether physical or conceptual, you are implementing a Game Mechanic.
Game mechanics are the the building blocks of a game. The basic actions players can make in a game. For example, a game can implement randomness in several ways: rolling a dice, card drafting, a spinning top, etc.
Some known mechanics:
See BGG-Game-mechanics, for the full list of game mechanics in board games.
Further reading: What are Game Mechanics