Game Mechanics are the overall frames upon which a game's rules are built. A game's rules are almost always built upon several mechanics (or frames) and two games built using the same set of mechanics will often play out differently depending on how the game designer has emphasized and combined them.
For example, Monopoly is primarily a game involving the roll and move mechanic, but set collecting is also an important part of this game.
From an educational perspective an understanding of these mechanics and how they can affect learning are critical for choosing the right game to use in class.