Ancient China, Mesopotamia, Ancient Egypt, Mesoamerica etc. Especially in more moderate areas where seasonal shifts aren't as noticeable.
I am not sure how to say this in a way that doesn't sound like I'm stating the obvious, but: because there are 365 days in a year.
A year is a very visible astronomical period, not just because of the seasons, but in the lengthening and shortening of days. If you're trying to keep time, counting the days between winter or summer solstices is an extremely obvious way to go about it.