Probably drawn from a major religion's, nation's, or culture's laws, habits, deities, or legends. Days might be named after saints, or famous heroes of the past, or famous kings, or acts/deeds of significance in the area's main religious text, or something else.
The Julian calendar's months are named after Roman emperors and something else I don't recall. The days of the week are largely drawn from Norse designations, for whatever reason (probably the mixing of anglo-saxons into other places after the Vikings settled down); Wednesday = Woden's (aka Odin's) Day, Thursday = Thor's Day, Friday = Frey's Day, etc.
I think the Chinese calendar's months are named after the Chinese zodiac animals, isn't it? (I don't recall) :\
In my Rhunaria homebrew, there's a calendar named the Common Measure, used by traders and most humans, halflings, gnomes, and a few other races, based on the year when independance was gained from the old regime that had control over the region. Days are just pidjin designations, months are named after some significant quality or habit of the season. The names of days, in order, are Dayun (day-
oon), Daytu (day-
too), Dayri (day-
ree), Dayir (day-
yeer), Dayev (day-
yevv), Dayas (day-
iss), and Dayan (day-
enn). As I said, just pidjin names the humans and halflings of different accents cobbled together for lack of agreement on other names (obviously, they're butcherings of the words one through seven, appended to 'day'). The eight months of the Common Measure, in order from 1st to 8th, beginning of spring to end of winter, are Fallow, Seeding, Suncrest, Heatwrath, Harvester, Gatherfast, Cloudblight, and Culling. Feel free to use the same if it suits your fancy.
The Elven, Dwarven, Tashi, Rizan, and other calendars are more complex and I haven't finished all the work on detailing them yet.