Literally,“good slide”, suggesting one slides into the new year.
An alternative suggestion is that it derives fromHebrewרֹאשׁ(rosh,“beginning”), clipped fromרֹאשׁ הַשָּׁנָה(rosh hashaná,“beginning of the new year”). (CompareHals- und Beinbruch, said to be from a Yiddish phrase.)[1]
Only used in the final days of December and up until midnight on New Year's Eve, after which other phrases such asfrohes neues Jahr are used.