Question
what happens to plants when the humidity levels are too high?

Answer
Dezi,
In some cases they die, especially succulents/cacti. On most plants too high of humidity will encourage fungal diseases to grow on them. Usually it is harder to control fungal diseases than insects. The best way to control fungal diseases is through prevention of them to begin with (add lighting, keep water off leaves & stems, etc.).
Good luck,
Rick in Southern NJ