The 2 festivals of a year that Chinese people burn spirit money (Also call joss bills, spirit bills etc).
1. Qing Ming Festival
(Qing Ming Jie)
Qing Ming is usually described as a festival of the dead, which takes place fifteen days after the spring equinox. Among the Hakka, however, this festival can last as long as a month, because tombs are scattered across the surrounding hills and must be swept according to generational order. For the first sacrificial visit, to the tomb of the founding ancestor, each segment of the lineage must send representatives; as the sweeping comes ever closer to the present generation, successive visits concern ever smaller groups. Each time, after the grasses have been cleared from the tomb and the offering set out, a cock is killed and its blood poured over "sacrificial money", which is then placed according to a fixed pattern on the outer, horseshoe-shaped 'rim' of the tomb. For this reason , Qing Ming festival is more popularly referred to by its characteristic act, that of 'hanging paper money [on the tomb]'.
(Source: Encyclopedia of Contemporary Chinese Culture;
Edited by Edward L. Davis. Publisher: Routledge UK, 2005, page 497)
On each Qingming Festival, all cemeteries are crowded with people who came to sweep tombs and offer sacrifices. Traffic on the way to the cemeteries becomes extremely jammed. The customs have been greatly simplified today. After slightly sweeping the tombs, people offer food, flowers and favorites of the dead, then burn incense and paper money and bow before the memorial tablet.
(Source: http://www.china.org.cn/english/features/Festivals/78319.htm)
2. Ghost Festival
(Gui Jie)
The Ghost Festival (Gui Jie) takes place in the middle of the 'ghost month': the fifteeth day of seventh month. In some parts of China, a 'ritual of universal salvation' (Pudu) is performed in order to save the souls of the unfortunate dead, lest they come back or linger and cause trouble. In Minnan-speaking areas (ie Fujian), for example, every temple and every street celebrates the Pudu. This ritual does exist among Hakka, but it is not a community festival: each family prepares, on its own, a sacrifice for the hungry ghosts. In Baisha (Shanghang, western Fujian), for example, people eat early that evening and then go to a crossroads to deposit a rice cake. Even more interesting, in Dongliu (Wuping, western Fujian), people write their own names and those of their ancestors on packages of spirit money which they then burn outside the gate; at the same time, but off to one side, they burn spirit money for the souls of the unfortunate dead.
(Source: Encyclopedia of Contemporary Chinese Culture;
Edited by Edward L. Davis. Publisher: Routledge UK, 2005, page 225-226)