[taregg (OP)]

doest mean the smallest size of element atoms or does it mean the smallest  hydrocarbon compounds chain...

[alancalverd]

It's the smallest molecule of a substance. Doesn't only apply to organic compounds, though they are the most commonly mentioned polymers. In fact water exists in many forms in the atmosphere, mostly as a monomer H₂O or a trimer (H₂O)₃ which accounts for its enormous and complicated infrared absorption spectrum.

Whether you refer to nitrogen N₂ or oxygen O₂ as diatomic molecules or dimers is in principle a matter of choice, but some would argue for instance that monatomic nitrogen N is much more reactive then N₂ so N₂ is a distinct molecule. On the other hand ethylene H₂C=CH₂ is clearly a molecule with much greater reactivity than polyethylene (H₂C=CH₂)_n.

[distimpson]

I've always used a functional definition, the monomer is the unit that is joined (condensed) to form the polymer. For example, polymethymethacrylate:


For a hydrocarbon like polyethylene, the monomer would be ethylene:


The definition can be context dependent if there is more than one way to make the same polymer.

Images from: http://pslc.ws/macrog/kidsmac/pmma.htm and http://www.innocalsolutions.com/