"Auld Lang Syne" is a Scots poem written by Robert Burns in 1788 often sung to celebrate the start of the New Year at the stroke of midnight.
The song's Scots title may be translated into English literally as "old long since", or more idiomatically, "long long ago","days gone by" or "old times". Consequently "For auld lang syne", as it appears in the first line of the chorus, is loosely translated as "for (the sake of) old times", presumably reflecting a common Middle Germanic/low Scots root; " Vor Alte Lange Zeit" (And thanks to Wikipedia for finally answering all my questions of what the term really means).
3... 2... 1... Happy New Year!