Adding a day to the end of the second month of the year in leap years might seem an odd choice. Of course it's the shortest month so makes sense to make it a bit longer on those years. But like many things there are historical reasons to it.
Our calendar, the Julian calendar system comes from Romans. It replaces the earlier Gregorian calendar system and there were other systems before that. The earliest Roman calendars actually started the year from March so February was the last month of the year.
While these calendar reforms were always challenging to implement they always retained some of the features from the old systems. Adding the leap day to the end of February was one of them even when the first month of the year changed. Hence we still keep adding the leap day to this seemingly arbitrary time when it was originally added as a last day of the year.