Why is there only 364 days in a year instead of 365 days?

It doesn't.

Earth's rotation around the Sun is about 365 days, six hours, and some - every year.

But since counting quarter-days would be so awkward, people cam up with the idea of adding one whole day every 4th year instead, to keep the calendar synched with the seasons.

Works just as well and is a lot simpler.

For those who need to be really accurate, there are even leap minutes and leap seconds that gets added every now and then.