The Hive Mind is the collective intelligence of every single logged-in player of Twitch Plays Pokémon. It is the Hive Mind that makes the ultimate decisions that control the character. Typically, the Hive Mind prefers to operate in anarchy, though democracy has been utilized for some relatively delicate tasks (such as giving a specific Pokémon a specific item). The Hive Mind was first heard in FireRed version due to a chat-to-speech option being added, many people spammed potato during this time.
A hive mind is the collective consciousness of multiple entities. While there are many individuals in a hive mind, the hive mind acts as though it were a single entity, leading to some odd and erratic behaviors done by the controlled character.
The Hivemind, in lore, is represented as the voices, Unknown who choose a host. When a user is banned, it's said that the Streamer destroys that voice.