Alumina (properly called aluminum oxide) powder as used in ceramics can be a white granular material (like table salt) or an exceptionally fine silky white and dense powder (depending on the type and processing method). 

In clay, alumina causes a flat crystal and gives the clay plasticity. In glaze, alumina stabilizes the fluxes and glass formers and affects the stiffness of the glaze when it is being fired. Too little of alumina has the glaze run but too much has the glaze pinhole and or crater. 

Information gathered from Digitalfire Ceramic Materials Database and The Potter's Dictionary of Materials and Techniques by Frank Hamer.