Translation:New Year's day is the first of January.
Calan (roughly "the first day") is a great word:
dydd Calan ("the first day") = New Year's Day
nos Galan ("the first night") = New Year's Eve
Calan Mai (the first day of May) = May Day
Calangaeaf (the first day of winter) = Hallowe'en
yr hen Galan (the old first day) = the old New Year's Day according to the Julian calendar, still celebrated in some parts of Wales like Cwm Gwaun
In Wales there used to be the tradition of calennig, a bit like trick or treating at new year.
Also of course is the related word calendr (calendar).