In the Gregorian calendar, the leap year is defined as any year whose ordinal number is divisible by 4. The years ending in 00 are an exception and are not leap years unless their ordinal value is divisible by 400. Thus, the years 1600 and 2000 are leap while the years 1700, 1800, and 1900 are not. This means that the sequence of leap years is repeated every 400 years. Because there are 365 days in a non-leap year, it consists of 52 weeks and 1 day (52*7 + 1 = 365). Therefore, if a given date is Monday one year, it will be Tuesday in the next year, and so on, moving up one weekday every year. On leap years, the date moves up by two weekdays. A quick look at a calendar spanning several years will convince you of this.
Suppose we select an arbitrary date, such as April 16, 1977, which is a Saturday. Based on the movement of weekdays established above, April 16, 1978 is Sunday; in 1979 it is a Monday; and in 1980 — a leap year — it is a Wednesday. In a 400-year period there are 97 leap years (three of the four years ending in 00 will not be leap) and 303 non-leap years. Therefore April 16, 1977 will "move up" a total of 303 + 97*2 = 497 days, or 71 weeks, again falling on a Saturday. Any date, including February 29, will fall on the same day of the week in any two years separated by a 400-year interval.
For more information on day-of-week, and calendars in general, see [1] and [2].