Our calendar system is based on how many times the earth rotates in the time it takes to do a full circuit of the sun. When it was first invented we didn’t know that was how we were measuring it. We used the stars and the seasons which just happen to be a result of the earth’s rotations/circuit.
The problem with this is that it doesn’t take a nice, even amount of rotations to do a full circuit of the sun. Apparently it’s 365.242199 days or so and that is why we round it off to 365 and throw in a leap year every four years.
365 is a crap number. It’s tricky to divide up evenly. In our past we convinced ourselves that there were four seasons in a year (which is like saying that a rainbow has six or seven colours) and so we tried to divide 365 by four and then into three for each month giving us a nice 12 months of 30.416666… days each month. Which means that some months have to be 31 and some 30 and then one adjustment month, February with 28 and sometimes 29 days. Add to this the fact that we’ve chosen to go with seven days in a week and you’ll see that 11 months of the year aren’t evenly divisible by weeks.
In 1849 Auguste Comte proposed the Positivist Calendar which did away with the notion of the four seasons but kept everything else and manages to do a pretty good job of it (if you trim off his peripheral ideas for the month names and for when the new calendar was to start). What he does is he divides 365 by 13 months of 28 days each which gives you every month starting on the same day with an even four weeks per month and one (two for a leap year) blank day at the end of the year. Brilliant!