Basically it comes from the roman calendar. Which is based on the sun and the moon cycles.

A year is a full turn around the sun. It takes 365,25 days. So 365 days, and 1 more once every four years.

A month is based on the moon revolution around the earth, which is 29,5 days.

But in the past they weren't as good to measure these times, so they used more approximative calendars that they would fix by adding days to synchronise the calendar on the moon or year. Roman for example had the month always start on a full moon.

For the months, you had then some emperors who wanted their month to get more days. I think the 7 days week comes from Christians, the bible talk about it. 7 days allows 4 weeks in one moon cycle. Roman used 10 days weeks, so 3 weeks in a moon cycle. Both are inaccurate, so there were days added or removed to synchronise regularly.

Julius Caesar basically made the calendar we have now because the old one was a mess. Then, in the XVIth century we got the gregorian calendar, which is almost the same but fix some problem the old one had.