How many days are there in a leap year?

A leap year has 366 days, one more than usual, and exists because the Earth does not orbit the Sun in a whole number of days. A year runs about 365.2422 days, so a calendar of 365 falls behind by nearly a quarter of a day annually. Adding a day every four years overcorrects slightly, which is why the Gregorian rule is more careful than most people remember: a year divisible by four is a leap year, except a century year, unless that century year is divisible by four hundred. So 1900 was not a leap year and 2000 was. Without the correction the seasons drift against the calendar, which is exactly what had happened to the older Julian system by the sixteenth century, when the spring equinox had slipped ten days from where the Church expected it and the date of Easter with it. The extra day is added in February.

Leap seconds are a separate correction, for the slight irregularity of the Earth's rotation rather than its orbit.