My plant has this white powdery looking dust on it. Why is it there, and what can I do?
From this description I would say it could be Powdery Mildew or Mealybug.
Mealybug is common on houseplants and can be treated.
Lightly wash the leaves and apply Neem Oil. Neem Oil works as both an insecticide and fungicide, it is also safe for people and pets.
Here are some links to help you.