Since February is the shortest month of the year, it was chosen to get an extra day in the leap year. The calendar can be changed to maintain the solar year in line with the calendar year by adding an extra day to February.
The solar year, which measures the time it takes for the Earth to complete one round of the sun, lasts about 365.2422 days. This indicates that if the year had exactly 365 days, the seasons would eventually start to move away from the calendar.
The leap year, which adds a new day to the calendar every four years, was created as a remedy for this. This extra day helps to keep the seasons in step with the calendar by bringing the duration of the calendar year closer to that of the solar year.
Because it is the shortest month of the year, having only 28 days in a regular year, February was chosen to have an extra day in the leap year. In a leap year, February is extended by one day, making the month 29 days long. This serves to balance the calendar and keep it in step with the solar year.