The solar year does not have whole number of days, but a calendar year must have a whole number of days. The only way to reconcile the two is to vary the number of days in the calendar year.
In many calendars, this is done by adding to a common year of 365 days, an extra day (leap day or intercalary day): this makes a leap year of 366 days.
The solar year does not have a whole number of lunar months either, so a lunisolar calendar must have a variable number of months in a year. This is usually 12 months, but sometimes a 13th month (an intercalary or embolismic month) is added to the year.
See calendar, Julian calendar, Gregorian calendar, Iranian calendar, Hebrew calendar, Hindu calendar, and Chinese calendar.