They send these out every once in awhile when something big has happened or may be about to happen - sort of like a travel advisory, but more targeted.
The most recent such note had to do with Saturday, April 14, the day on which several political movements, including the opposition, decided to hold rallies all at once. Below is a rather informative excerpt:
[...] The Russian Ministry of Internal Affairs has advised the U.S. Embassy in Moscow of several large demonstrations planned for Saturday, April 14th in Moscow at the locations listed below. Moscow city authorities do not rule out the possibility of violence, and will be providing a large militia presence, particularly in the area of Pushkinskaya. The Russian authorities advise Americans to avoid downtown Moscow on Saturday, or to exercise caution if you must be in the area. We wish to remind American citizens that even demonstrations intended to be peaceful can turn confrontational and possibly escalate into violence.
The times and locations are as follows:
12:00 PM - Pushkinskaya Square, Sparrow Hill, and Turgenevskaya Square – Molodaya Gvardia and Other Russia, expecting up to 20,000 people.
1:00 PM – Slavyanskaya Square – Union of Right Forces.
2:00 PM – Bolotnaya Sqaure - Movement Against Illegal Immigration and Congress of Russian Communities, unlikely to draw as large a crowd. [...]
While a few hours still remain before the busy "demonstration day" begins, a good (if somewhat carefree) question to ask is this: Why April 14?
At least one Russian blogger - LJ user galerist, gallery owner Marat Guelman - hosts a discussion (RUS) on this subject on his blog:
I'm not reading newspapers and that's why I learn about the news from journalists who ask me to comment on this news. And yesterday, for example, I learned that four rallies are scheduled for April 4. Rallies of those who agree and those who don't, CRC and URF.
Please educate this ignorant one: why April 14? What's in the date? [...]
vianega: April 14 - because it's Saturday, and the next weekend will be Lenin's and Hitler's birthdays, dangerous. [...]
panam: And no one got an idea to hold a rally against all these rallies on Friday the 13th... [...]
jfht: There was an idea to have a protest rally against protest rallies, only I don't remember if it did take place. [...]
gleza: April 14 is the day on which poet Vladimir Mayakovsky committed a suicide.
galerist: I wonder if anyone would remember this.
leprikon: I'm turning 30 on April 14. It's terribly unfair and I disagree with it, too. :)
galerist: Sounds like a reason for the fifth rally.
katterfeld: We in Irkutsk are also holding it on the 14th: http://babr.ru/?pt=news&event=v1&IDE=37047.
The logic is simple: a week earlier is still cold; a week later, there are Lenin's and Hitler's birthdays, and Nazis and Communists would be getting in the way; and then there are May 1, May 9, and the dacha season...