A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December.
Any leap year that starts on Monday has two Friday the 13ths: those two in this leap year occur in September and December.
Common years starting on Tuesday share this characteristic.
Leap years that begin on Monday, along with those starting on Saturday and Thursday, occur least frequently: 13 out of 97 (≈ 13.4%) total leap years in a 400-year cycle of the Gregorian calendar.
Like all leap year types, the one starting with 1 January on a Monday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years.