Chewing through /u/cthulhushrugged's excellent History of China Podcast currently, there's a repeated theme of empress dowagers overreaching with their power leading to the downfall of a dynasty, in particular during the centuries of disunity starting with Eastern Han. I recall there was an instance in Jin (?) Dynasty where the empress dowager actually need to sign off for an imperial edict to take effect. What official capacity do Empress Dowagers had in Imperial China that allowed for such power grab to take place?
Powerful empress dowagers are always portrayed very poorly, is that purely propaganda, or there's something to it?
This is a big question, and I'll try to answer it broadly first. So for much of this answer, I'll be referencing the "first" of China's powerful empress dowagers, title 宣太后 (Empress Dowager Xuan), who reigned in the 250-260 BC era. She's mother of Emperor Zhao of the Qin dynasty. She's quite special not only because she's the "first", but later Empress Dowagers and powerful female politicians in general would use her as justification of the legitimacy of a female ruler.
There are generally two reasons why the Empress Dowager played a domineering role in ancient Chinese court.
First, we need to realize that filial piety is a central tenet of Chinese philosophy. (further reading : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.831.3178&rep=rep1&type=pdf) This meant that there's a lot of importance placed on one's parents, especially the mother. If the Emperor wanted to be seen as someone who is filial pious, he had to give respect to his mother and thereby legitimize her position in court. In the case of Empress Xuan, much of the court saw her initially as a powerful lobbying force who could affect the Emperor. In this case, the Emperor showed "respect" and placed her in high regard by consulting her on every political issue he came across. And as the Emperor relied more and more on her, he further legitimized her role in court, she became a political party of her own, even eclipsing that of the Emperor.
Second, in order for the Empress Dowager to grab power, the Emperor must be weak. In all instances in China of the Empress Dowager reigning, the Emperor was either not yet of age or incredibly passive and easily controlled. When the Emperor is weak and unable to assert full control of his court, there would exist a power vacuum. Generally, in such a case, the one who benefits is the person closest to the Emperor, who sorts things out in his stead. Due to the aforementioned filial piety, that person is usually the parent. Since the current Emperor's father is most likely dead, that role generally falls to the mother. In Empress Xuan's case, when her son, Emperor Zhao took the throne, he was young and unable to fully take control of the court itself. The court would not respect his decisions because of his age, and so rather than allow a third party to dominate the court, Empress Dowager Xuan herself stepped in. She used her position as the Empress Dowager as well as her experience in politics to legitimize her decisions, and the court, though none too happy, were obliged to obey in absence of a clear contender.