In the games
Dream Mist is unable to be obtained by the player in Black and White, but it is an important part of the storyline. After obtaining the Trio Badge, the player is asked to fetch some Dream Mist from the Dreamyard by Fennel, a scientist. However, Team Plasma also wish to obtain Dream Mist, and must be defeated before the Dream Mist can be recovered. After they are scared off by a wild Musharna, Fennel is able to recover her Dream Mist.
In the anime
The Dream Mist appeared in the anime in Dreams by the Yard Full!. The Musharna living in the Dreamyard sent it out in huge clouds, causing Dream Mist to fall over Striaton City and put Pokémon to sleep. One of the victims was Iris's Axew, but Fennel's Munna was able to heal him by inhaling the Dream Mist that covered Axew. Munna's floral pattern then turned pink as Munna expelled a puff of mist revealing Axew's dream of evolving into a Haxorus.
In the end, Fennel and her Pokémon were able to stop the Dream Mist from putting all the Pokémon to sleep.
In the manga
In the Pokémon Adventures manga
Dream Mist was first mentioned by Fennel in Fussing and Fighting where she calls Professor Juniper to tell her about it. Dream Mist doesn't make an actual appearance until Black is defeated by N in Accumula Town. After N leaves, Black mentions to White that his Musha captured some of N's dream and produced an image of it through its Dream Mist.
Later, Musha had gotten separated from Black after wandering off. Black met Fennel after being knocked out cold, and Fennel offered to help him find Musha in the event that she could examine it. Black agreed and once they had successfully retrieved Musha from a few Team Plasma Grunts, Fennel was able to collect some of Musha's Dream Mist after he had eaten Black's dream.