'Fat Tuesday' is the English translation of the French term 'Mardi Gras'. And there are two ways people participate in this annual tradition. One is with religious ritual and observance. The other, one big ol' party. Of course, if you consider the amount of people all over the world that participate in this tradition and plot them on a venn diagram, a good portion would fall into that overlapping, middle area that think of it as both a time to let loose, and as part of their religious obligation.
In the Western Christian tradition, Fat Tuesday (Mardi Gras) is the calender day directly before Ash Wednesday. And Ash Wednesday is the first day of Lent, the 40-46 day period between Fat Tuesday and Easter. During the period of Lent, Christians practice differing variations of abstinence, fasting and prayer. A common practice is to pick something in your life that you would be really bummed out not to have or do for the next six weeks or so, and to basically not consume or do that thing. One popular example would be giving up chocolate, sugar, meats, alcohol, cigarettes, or sex. Since 40 some-odd days is quite a long period of time, many following this tradition consider the Sundays in between a cheat day, and only avoid whatever it is they've sworn to avoid for 6 days out of each week of Lent. Others are more strict.
Fat Tuesday's name comes from the ritual of eating richer, fatty foods the night before Ash Wednesday. Basically, it was a way to gorge yourself on calories just before you started a month and a half of barely eating at all, kind of like what a bear does just before hibernation.
As with most religious traditions, Fat Tuesday has morphed and evolved over the last 1000 years or so. When someone thinks of Fat Tuesday or Mardi Gras today, it's hard for most not to think of the lavish New Orleans' parades, beads, girls flashing mobs of drunk people, chaos, and good times, crazy memories of "that one night...". Fair enough. New Orleans does host the biggest celebration of Mardi Gras in the world, an all-out party scene that lasts an entire week, not just one night. The last night of Mardi Gras for New Orleans is still Fat Tuesday; they still follow the calender of the original tradition there. Difference is, when the Big Easy celebrates Fat Tuesday, that last 24 hour stretch caps off a week-long marathon of excessive drinking, eating, partying, gambling and bead distribution of the highest order. It's the original idea of the French's Fat Tuesday, times about a million. And that week-long binge does very well for the city; its estimated to bring around $1 billion dollars a year into their economy. That's one profitable week indeed.
New Orleans isn't the only city in the U.S. that celebrates a week long Mardi Gras party, or even a day long Fat Tuesday. Virtually every city in our country participates in some form or fashion, from the pious and low key, all the way to something that attempts to emulate the Big Easy on both scale and excess.
Mardi Gras is celebrated all over the world actually. I just focused on the Western tradition in this piece because a majority reading are largely English speaking westeners. For a full breakdown of how the rest of the world does Mardi Gras, and for a deeper and more comprehensive history, check out these links below:
Wikipedia on Mardi Gras
Carnival Around the World
French roots of Mardi Gras; celebrations around the world