Where does the name ‘aliphatic’ come from? Generally, carbons and the hydrogens bonded to them are classified as one of the following:


aromatic
olefinic
aliphatic
(something for triple bonds I don’t know)


The meaning of aromatic is rather clear to anybody: They belong to aromatic systems (even though the Hückel rule has nothing to do with a certain type of smell). Olefinic is also clear enough: Olefins were originally those gases which could generate an oily substance by reaction with e.g. chlorine ($\ce{C2H4 + Cl2 -&gt; C2Cl2H4}$; the latter being 1,2-dichloroethane); the name olefin derives from French gaz oléfiant — oil-creating gas.

But I have no clue where the adjective aliphatic or the noun aliphat derive from, which are applied to saturated carbons. What was its original meaning and why do we use it?
Olefins are hydrocarbons that contain at least a double bond. The term is used &mdash;sometimes misleadingly&mdash; interchangeably with alkenes.


  Although the nomenclature is not followed widely, according to IUPAC, alkenes are acyclic hydrocarbons with one double bond between carbon centers. Olefins comprise a larger collection of cyclic and acyclic alkenes as well as di- and polyenes. &mdash; Alkene nomenclature &ndash; Wikipedia


The Goldbook page Wikipedia cites says the final words:


  Olefins
  
  Acyclic and cyclic hydrocarbons having one or more carbon–carbon double bonds, apart from the formal ones in aromatic compounds. The class olefins subsumes alkenes and cycloalkenes and the corresponding polyenes.


While Oxford dictionary seems to agree with the origin thingy:


  Origin
  
  Mid 19th century: from French oléfiant 'oil-forming' (with reference to oily ethylene dichloride).


Funny thing is, "aliphatic" also means "producing fats". Goldbook says:


  aliphatic compounds
  
  Acyclic or cyclic, saturated or unsaturated carbon compounds, excluding aromatic compounds.


Some definitions exclude alicyclic compounds from the list of aliphatic compounds, but IUPAC doesn't agree, so. Note that aliphatic compounds can be saturated or unsaturated.

So, back the main answer part,


  Aliphatic; Etymology
  
  From Ancient Greek ἄλειφαρ ‎(áleiphar, “oil, ointment”). &mdash; Wiktionary


There are literally no articles on the Net speaking of the first discovered or documented aliphatic compounds, but I read in some textbook somewhere which mentioned that since these compounds were first referred to as what animal fats used in primitive or medieval lamps were consisted of, they're referred to as "aliphatic".

The only thing about a "first aliphatic" I could find is mentioning "Muconic acid is the first aliphatic compound formed as a result of aromatic ring splitting, which is further oxidized to fumaric acid and then participates in the cell metabolism as a standard endogenous substrate." by this paper.