Leap year
The name "leap year" probably comes from the fact that while a fixed date in the Gregorian calendar normally advances one day of the week from one year to the next, the day of the week in the 12 months following the leap day (from March 1 through February 28 of the following year) will advance two days due to the extra day (thus "leaping over" one of the days in the week). For example, Christmas Day (December 25) fell on a Sunday in 2016, and Monday in 2017, then it fell on Tuesday in 2018, and will fall on Wednesday in 2019 but then "leaps" over Thursday to fall on a Friday in 2020.
Leap year starting on Saturday
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. As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).