The full story is here. I'm posting a brief excerpt, but I encourage you to go to the source and read all about it.
Read An RPG Book in Public Week is an event that happens three times a year, during the weeks surrounding March 4th, July 27th, and October 1st (starting on the Sunday on or before, and ending on the Saturday on or after). During these weeks, roleplaying enthusiasts are encouraged to take their favorite RPG rulebooks out with them and read them in public - on the bus, in the coffee shop, at lunch, at the park, or anywhere (as long as it isn't disruptive to work, school, church, or any other functions).
What's the point?
The point is to make the roleplaying hobby more visible, to get it "out of the basement" and into public areas where more people can see it. This will make others more aware of the hobby - some may ask you what your book is about, giving you the opportunity to explain the hobby to them. A few of those may be interested enough to try it themselves. Former gamers may see what you're reading and think about the great times they used to have with roleplaying, and possibly even try it again.
Me again. I'm also reminded that March 4th is GM's Day - ENWorld created the holiday in 2002, and, sadly, Gary Gygax died on that date in 2009. Players, say something nice to your GM on March 4th.