[fú] character means "fortune" or "good luck".
Posting the "福" character is a tradition for Chinese people during 春节
[chūn-jié] Spring Festival each year.
The "福" character is often posted upside-down. It is said that this is because the character for "upside-down", "倒"
[dào], is a homonym of the character for "to arrive", "到"
[dào]. So this means that "福" (happiness, good fortune, etc.) is "arriving". (source)
It also said that Emperor 朱元璋 (Zhu Yuanzhang), a founder of Ming dynasty, once used the character "福" as a hidden signal to prepare killing someone.
The kind-hearted Empress Ma decided to eliminate the tragedy of killing, so she ordered everyone in the city to put a label with the character "福" on the door of their house before the sun rises the next day. Everyone followed Empress Ma´s order, but one family is illiterate and pasted the label with the character "福" upside down.
On the second day, the emperor ordered his officer to go to the city and found that every family had pasted the label with the character "福", and with one family having the character "福" upside down. The emperor was very angry and ordered that family be executed. Empress Ma realized the incidence and told the emperor, "that family knew you´re coming today, so purposely turn the label upside down. Isn´t that the same meaning as Luck arrives?"
After hearing this, the emperor immediately released the family and a tragedy was averted. From then on, people began to paste the label with the character "福" with the purpose of hoping for auspiciousness, and another to honor Empress Ma.