The German word "rutschen" means to slip or slide.
But, if in December Germans wish you a "Guten Rutsch!" ("Good slide!") they don't want you to go on a slide or slip on black ice.
They wish you a nice New Year's Eve and turn of the year.
The complete saying is "Guten Rutsch ins neue Jahr!" ("Good slide into the new year!") but almost everyone just says "Guten Rutsch!"
(It's not the same as "Happy new year!" which would be "Frohes neues Jahr!")
So, enjoy our language - and your "Rutsch"!