The plant is healthy otherwise, I see a few ants crawling around on it. Is this a sickness? How do I remove this and get shiny leaves like I see others have?
The plant is a ponytail palm or Beaucarnea recurvata a member of the Asparagus family and native to Mexico. The identification is the woody trunk and the long curved leaves. The pest is mealy bug. It also appears to have some hard water deposits or pesticide residue as some of the white stuff is flat on the leaf and some is fuzzy. See here for a similar problem on a different plant.
You can try to control the mealy bug but it's hard because they hide deep in the axils of the leaves
Other maintenance measure if you decide to keep it