These moves are based on dancing. Pokémon with Dancer can copy these moves when used by another Pokémon. In Pokémon X and Y, Tierno will request to see a Pokémon that knows one of these moves once per day during the post-game in Coumarine City.
In particular, Rain Dance is not a dance move, because its Japanese name means "Rain Prayer" instead. As such, Tierno does not request to see a Pokémon with this move in Pokémon X and Y, and this move is not copied by Dancer.