Short answers, pulled from the story.
Game mechanics are the rules and ludemes that govern player actions and the game's responses; a game's theme is its representational layer, what the events stand for. Monopoly's mechanics govern turn-taking and property ownership, while its theme represents buying and selling real estate. Two games can share mechanics while having entirely different themes, or share a theme while working through different mechanics.
A ludeme is an element of play, such as the L-shaped move of the knight in chess. The term distinguishes a unit of play from a rule, which is an instruction on how to play. Game mechanics are understood to consist of both rules and ludemes working together.
Worker placement is a mechanic where players allocate a limited number of tokens to stations that each provide specific actions. Stewart Woods identifies Keydom, released in 1998 and later remade as Aladdin's Dragons, as the first board game to implement it. Caylus, released in 2005, popularized the mechanic and made it a defining feature of the Eurogame genre.
A single die produces a linear probability distribution, meaning every face is equally likely. Rolling two or more dice and summing the results produces a bell curve, with middle values occurring far more frequently than extreme ones. Adding more dice steepens the bell curve further, making extreme results increasingly unlikely and the outcome feel more predictable to players.
Ludonarrative dissonance is the tension that arises when a game's mechanics and its theme pull against each other. The term describes the friction a player experiences when the story a game tells conflicts with the actions its rules demand.
Capture mechanics include replacement capture, where a token moves into a space held by an opponent as in chess; jumping, where a token leaps over an opponent as in draughts; custodian capture, which surrounds a token on adjacent squares as in tafl; and enclosure, which surrounds a region entirely as in go. Captured tokens may be permanently removed, as in chess, or kept and redeployed by the capturing player, a process called conversion used in Shogi, Reversi, and Illuminati.