Holds liquid or gases (usually ingredients or potions)
Phials are containers which usually hold liquids or gasses. Most potions and potion ingredients are bottled in phials and are consequently sold in those amounts.
One set of glass or crystal phials are part of the required equipment for classes at Hogwarts School of Witchcraft and Wizardry. One place first-years can aquire them are in Wiseacre's Wizarding Equipment in Diagon Alley: glass phials cost three Galleons and crystal phials cost seven.
There are quite possibly many different sorts of phials, but the to known sorts are made of glass and crystal.