Hybrid Berries are simply berries that have mutated due to being next to each other.
Mutation will sometimes occur when two different types of Berries are grown next to each other. Once a certain mutation has been performed once, the formula for it can be reviewed with the Scientist in the Berry grower's hut. Using Surprise Mulch or Amaze Mulch on the trees involved increases the chance of a mutation.
You can also view the possible combinations provided in my source!
Hopefully this helps!