The New Year period, especially the first few days (traditionally the first three days) after New Year's Day.
正月は家族と一緒に過ごして、おせちを食べる。
I spend the New Year with my family and eat osechi (New Year dishes).
正月三が日は神社に初詣に行く人で賑わう。
Shrines are crowded with people visiting for the first shrine visit of the year during the first three days of the New Year.
田舎では正月になると親戚が集まる習慣が残っている。
In the countryside, the custom of relatives gathering for the New Year still remains.
The first month of the year; January.
今年の正月（＝1月）は雪が多かった。
This January there was a lot of snow.
正月の予定はもう決めましたか？
Have you already decided your plans for January/the New Year?