The song's, Auld Lang Syne, Scots title may be translated into standard English as "old
long since", or more idiomatically, "long long ago” or "days gone by" or "old
times". Consequently "For auld lang syne", as it appears
in the first line of the chorus, might be loosely translated as "for (the
sake of) old times".
On the second stanza of the song, they should not forget the cup of kindness they've shared.