The song that millions of people sing on New Years Eve is a Scots poem written by Robert Burns in 1788 and set to the tune of a traditional folk song. However, Burns never claimed that he was the original author. Instead, he once wrote, "I took it down from an old man." In fact, the ballad "Old Long Syne" printed in 1711 by James Watson shows considerable similarity in the first verse and the chorus to Burns' later poem and it is assumed that even Watson's version was not the original.
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". "For auld lang syne", as it appears in the first line of the chorus, is loosely translated as "for (the sake of) old times".
Singing the song on Hogmanay or New Year's Eve very quickly became a Scots custom that soon spread to other parts of the British Isles. As Scots (not to mention English, Welsh and Irish people) emigrated around the world, they took the song with them.
You can read a lot more about Auld Lang Syne in Wikipedia at http://en.wikipedia.org/wiki/Auld_Lang_Syne