Generation refers to the Pokémon game series. It is a group of games that were released at or around the same time. It also means that games in the same generation are compatible with the others, containing the same Pokémon and the number of moves there are to be learned. For example "Pokémon FireRed and LeafGreen", though set in the same time period and region as "Pokémon Red and Blue", are not considered to be Generation I games. This is because they were released years after the original and have many new features and differences, which makes them incompatible with the original. Since they have the same features as "Pokémon Ruby and Sapphire" and were released around the same time, they are considered Generation III games.
Along with this, games in different generations have different features and/or game mechanics.