Why is the IUPAC name of glycerol expressed in the way that it is?
Glycerol and trihydroxypropane are common names. The IUPAC name is propane-1,2,3-triol. The common name glycerol comes from the root glyco- which means sweet. Glucose, glycogen, and glycerin (another name for glycerol) have the same etymology.

Trihydroxypropane makes sense as a common name because there are only 3 locations for the hydroxyl groups on the 3 carbon chain, so the name is basically unambiguous - multiple hydroxyl groups on the same carbon are not stable (see geminal diols).