Steam Summer Adventure 2014 is a special set that was made available during the 2014 Steam Summer Sale, which ran from June 19 to June 30. Beginning on June 10, crafting any badge gave you a Mysterious trading card. When the sale began, the cards changed into this set.
During the sale, cards can be earned by crafting any badge, voting 3 times on the community's choice vote or by purchasing games from Steam ($10 US per card.) For more information, visit the Steam FAQ about the sale.
During the sale event, players were divided into 5 teams which competed for points based on crafting badges. More information about that can be seen here.