A Grand Lodge is the central administrative and chief authority for the governance of all lodges in a given jurisdiction. They are sovereign in that they owe no explanation or obedience to any other Grand Lodge.
In many countries, there is one Grand Lodge. Sometimes there are more than one. Which one is "legit" depends on whom you ask, but generally, it will be the one -- or ones -- that can trace their formation back through time to the United Grand Lodge of England, formed in 1717, in London.
Some Grand Lodges do not require a belief in a Supreme Being -- and these are considered irregular because they do not conform to one of the great Landmarks of the Craft -- those practices or basic features that define what Freemasonry is. Such a Grand Lodge and all lodges under such a Grand Lodge would not be recognized by other regular Grand Lodges.
Then there are individual lodges that are clandestine, meaning that they were formed without a proper warrant or dispensation from the Grand Lodge under whose jurisdiction they would be. They may be regular inasmuch as they adhere to the Landmarks, but having failed to incorporate in adherence to Masonic Law, they would not be recognized. It would be possible for a clandestine lodge, if regular, to become recognized, by applying to the proper Grand Lodge. Most clandestine lodges I have heard of are also irregular in some way as well.
Large countries that they are, in the USA, Canada and Mexico, there is a Grand Lodge in each state. Mexico is more complex, because there are often several Grand Lodges in a given state and much political wrangling.
You may have heard of Masons traveling to visit a lodge in another grand jurisdiction and having to prove he is a Mason. This is a very ancient practice - and having a membership card and a driver's license to prove that you are who you say you are, are not enough. Masons have modes of recognition that derive from the days of illiterate, traveling stonemasons who had to protect guild secrets and also show their level of skill as workers. One book that discusses this in some detail is Ross King's Brunelleschi's Dome.
It's a lively book that brings to life what it would have been like in those days when Freemasonry was taking shape, becoming what we know it to be today. Yes, there are differences from place to place in terms of ritual, for instance; but those differences are slight -- and as long as the ancient landmarks are preserved, their members will be recognized by other Masons the world over.
You may be wondering "why all the fuss?" It may seem a bit like the Dr. Seuss story of the Sneetches, but Freemasonry is a serious organization with a lot of pride in the antiquity of its practices and zealously protects them from what one could call erosion, cultural decay or just plain dumbing down. Hence all the concern over regularity and only being in Masonic communication with regular Grand Lodges and the lodges under them. It may sound a bit like, say, the Anglican Communion, and the comparison is good up to a point -- but we are a fraternity, not a religion. Our rituals are not performed to grant sacramental graces, like baptism.
