The reason February has 28 days is disputed. Here is some history:

The Western calendar has been developed from the Roman calendars. Originally, the Roman calendar had 10 months (the names of some of the months, namely September through December, are relics of this calendar as September indicates the seventh month, etc...) The time from December to March was not on the calendar.

A Roman emporer named Num Pompilious added 2 more months with a total of 355 days, with a number of intercalary days (days off the calendar) added to keep in time with the seasons.

Julius Caesar reorganized the calendar, adding 10 days for 365 days and adding an additional month. This month, February, had 29 or 30 days as days needed to be periodically added to keep time with the seasons. (These are called leap days.) Eventually the calendar order was written as presently done with January the first month and December the last month.

The Julian calendar still lost a day every 128 years, so in 1582 the gregorian calendar was issued. (Named after Pope Gregory.) This calendar runs from January to December with February having 28 days in regular years, and 29 days in leap years which occur every 4 years unless it is a year that is divisible by 100 and not 400.

So why 28 days? There is a belief that the number of days was shortened from 29 to 28, with the missing day added to August. Thus August, named for Augustus Caesar, would have as many days as July, named for Julius Caesar.

Another possibility is the Roman belief that even numbers were unlucky. So the original calendars had months with 29 or 31 days. In order to make 355 days, one of the months needed to have an even number of days so the newest month, February, was selected and made relatively short.