Stellar, Solar, Lunar, and planetary cycles all have an impact upon cultures. They are convient ways to mark the passage of time. Marking the passage of time is VERY important if you are in the agricultural OR ritual business. Heck, some said the existance of "ritual business" was initially required the organization of agriculture. The "folklore" that crop people used to mark time evolved into religion (or was folded into the existing religious order).
Most everyone has a day night planetary period. If you have a center earth sort of world, with an eternal sun, you will need a moon or something to create a sense of time. If you don't the world is timeless or has minimal concept of time passing (See Warlord Comic Book or Pelucidar books).
The Passing of seasons (planetary cycle) is an important element for agriculture. If you are lucky some lunar, solar, or stellar event that you can notice, is there for you.
If a culture puts an emphasis on Lunar cycles, the "calander" will be lunar in nature. Two (or more) lunar cycles might mean you have a linked set of months. much like we have weeks and months, they have two months.
If your moon's period is not its cycle, you will have a moon whos face is always changing. There may be a "week" or sub unit of a month based on the rotating face.
If you are lucky, your lunar calander works out to be the same as a solar calander. If not, your calander falls out of synch with reality... causing problems for the ritual and agricultural business... as they are supposed to plant crop X on the 12th day of spring, but their calander is 32 days off, so it is the 44th day of spring when they actually plant.
This is what brought about the Gregorian Christian Calander, so Easter and other holidays would occur when they should occur.
For the West, accuracy was more important than tradition. In China, the Lunar Calander was maintained (augmented by a solar calander.. rather than replaced). The Aztec and Mayans used both a solar and lunar calander that were seperate from each other. Thus they had special days when the calanders linked up ever 52 and 725 years.
If you are lucky and have other period celestrial bodies to observe (A pulsar nearby) the rotation or cycle of other planets, comets, etc, you might have calanders based on that.
The passing of time become inportant for agricultural, religious, and administrative/ ruling functions. So make sure your world has a calander and you know why they selected that calander.