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A cryptographic scheme that lets you verify a round was decided before you bet and not altered afterwards. It proves the result was not manipulated. It does not change the house edge, which remains exactly as published.
A random string the casino generates and commits to by publishing its hash before you play. Revealed after the seed is retired so you can confirm it matches the hash you were shown.
A value your own device contributes, and which you can usually change. It exists so the casino cannot control the outcome alone.
A counter that increments with each bet, making every round unique even when the seed pair does not change.
The keyed hash function most provably-fair systems use to combine the server seed, client seed and nonce into a result. Deterministic, so anyone with the three inputs can recompute the round.