Listen to "Auld Lang Syne" 

syne: ago.  "To a native of this country it is very expressive, and conveys a soothing idea to the mind, as recalling the memory of joys that are past" (Jamieson, quoted in Kinsley 3. 1291).

You know it.  You love it.  But what's it mean?  Its annual use to ring the old year out & and the new year in makes it Burns' best known poem.

Burns claimed that this was an old folk song that he wrote down.  How much he revised it is uncertain.

So what makes this the perfect New Year's Eve song?  Several factors (Crawford 320-322).

1. It is a drinking song.
2. It celebrates the past.
3. It is a song for groups.  The celebration of memories of the past is a communal one; the recollection is shared.
4. It "celebrates both friendship between man and man [fiere, friend] and affection between man and woman [jo, dear]" (Crawford 320-321), that is, it encourages random kissing.  The "cup o' kindness" is a drink shared by men & women, while a "right guid-willie-waught" is a "good stiff drink" toasted among men.  "It means a drink shared as a token of mutual good-will, with undertones of mingles hospitality and ceremony" (Crawford 322).
5. The song's genius is that singing it develops the emotions it celebrates.  Plus you only hear it once a year, so you don't get sick of it.

Kinsley, James.  The Poems and Songs of Robert Burns.  3 vols.  Oxford: Clarendon Press, 1968.