Glycerol

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Chemically

Glycerol - a clear, viscous, odourless, slightly sweet, non-toxic, liquid

used e.g. as a humectant, a solvent, a sweetener, a preservative, a thickening agent

has some anti-freeze properties

has a few medical uses

A specific compound (C₃H₈O₃), and technically a triol (with three OH groups)

Glycerol and glycerin (US) / glycerine (UK) refer to the same molecule, but glycerin is a commercial term that typically refers to mixes that are mostly (>95%) glycerol.

See also:

• https://en.wikipedia.org/wiki/Glycerol

More widely, you can look at diols and triols.

You may see the term glycol[1], which is the property/grouping of aliphatic diols, where

aliphatic = non-aromatic

diol = alcohols with two OH functional groups (triols have three)

Some compounds in this area include (but are certainly not limited to)

glycerol (E422), as mentioned

propylene glycol, somewhat similar to glycerol

E1520 when used for food

E490 when used for cosmetics

ethylene glycol (used in classical antifreeze, and toxic)

Uses

Smoke machine fluids were often basically just glycerol (sometimes other glycols, but not ethylene glycol) and water, though there appear to be some newer formulations that leave less residue(verify).

Vaping liquid has a base that is often a mix of part glycerin (smoother, cloudier) and propylene glycol.

Used as a sweetener, humectant, preservant, and is used in personal lube.