Not just an ice cream flavor!
"Vanilla" refers to the original, unmodded assets of a game. Vanilla Stardew Valley, for example, would refer to the game as it comes from the store, with no unofficial content added. The name derives from the association that vanilla is a mild flavor to which things (chocolate, caramel, strawberry, etc.) are often added.
As examples, "vanilla tile sheets" are the tile sheets the game comes with and "vanilla dialogue" is dialogue spoken by an NPC in the original game. A vanilla NPC would be one included with the game (e.g., Marnie, Shane, Grandpa) versus a custom NPC (e.g., Stardew Valley Expanded's Sophie, Ridgeside Village's Kiwi, etc.) If someone used a randomizer to shuffle the community bundles, but ended up with items that were the same as the original game, they would say it was a vanilla bundle (and would likely make a joking comment about "Is this even randomized?").