There is a debate among the Muslim community on just how to calculate the beginning of the month of Ramadan (or indeed any month, but Ramadan takes on special importance).
The traditional method, mentioned in the Qur'an and followed by the Prophet Muhammad, is to look to the sky and visibly sight the slight crescent moon (hilal) that marks the beginning of the month. If one sees the hilal at night, the next day is the first day of Ramadan and thus the first day of fasting. At the end of the month, when the community sights the hilal again, the Festival of Fast-Breaking ('Eid al-Fitr) begins.
Questions and debates have arisen around the following questions:
What if people in one area sight the moon, but those in another area don't? Is it okay for them to start and end the fast on different days?
Should we follow the moon-sighting in Saudi Arabia (or any other area of the world), or should we in our local community sight it ourselves?
What if our location is overcast and cloudy, and the moon is not visible to us?
Why do we even bother looking for the moon, when we can astronomically calculate when the new moon is born, and thus when the crescent should be visible? That eliminates human error, right?
Over the years, various scholars and communities have answered this question in different ways. The prevailing opinion is that one should commit to a local moon-sighting, i.e. begin and end Ramadan based on the sighting of the moon in your local vicinity. Astronomical calculations can help us predict when the moon should be visible, but Muslims still tend to follow the traditional method of looking at the sky themselves and physically "sighting" the moon. Thus, the exact day of the beginning of Ramadan is not generally known until the night before the fast begins, when the moon is actually sighted and confirmed.