A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December.
Common years starting on Sunday share this characteristic, but also have another in January.
These types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Sunday is considered the first day of the week, and also the only type of year to contain 53 full weekends.
Leap years that begin on Saturday, along with those starting on Monday and Thursday, occur least frequently: 13 out of 97 (≈ 13.402%) 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 Saturday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years.