Hello, thanks for using ask an expert. The specks on your plant are either mealybugs or scale, two types of insects that sit in one place on the plant and drink the plants juices through straw-like mouthparts.
Mealybugs are fairly easy to remove with an alcohol-soaked q tip (rubbing alcohol). Scales are usually a bit tougher, the adhere to the leaves with a sticky substance that they exude from their bodies.
http://manatee.ifas.ufl.edu/lawn_and_garden/master-gardener/gardening-manatee-style/s/scale-insects-...
The above link takes you to University of FL's site about these insects on house plants. You should get great info there on how to deal with this pest. Thanks again and best wishes,
Nicole