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A 'common year' is a year that is common calendar year. It has exactly 365 days and so is not a leap year. More generally it is a calendar year without intercalation.
A common year of 365 days has exactly 52 weeks and one day, so consequently the next new year is one day of the week later.

★ 2001 began on a Monday.

★ 2002 began on a Tuesday.

★ 2003 began on a Wednesday.

★ 2004, a leap year, began on a Thursday.

★ 2005 began on a Saturday.

★ 2006 began on a Sunday.

★ 2007 began on a Monday.
In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years were common years.