The concept seems very similar to the western idea of divine right to rule, but that rule was seen to come from a specific source/personality (i.e. God). Since there doesn’t seem to be a tradition of a discrete pantheon in the east as in the west (at least that I’ve understood), what entity is seen as granting this power?
Heaven in the Taoist sense is above - the sky. Above the sky, to be exact. When things are said to abide in the heavens, they are refering to the stars themselves. Taoist astrology has rules and divination ceremonies for many star events, significantly shooting stars will be a sign of things such as a new king or impending death. This plays into the Mandate of Heaven because these seemingly insignificant events gain additional importance when combined with Taoist ritual ceremonies, especially when combined with some of the architectural curiosities which Taoist temples intentionally create.
This includes cardinal directions, specialized importance in stars for navigation, and Taoist priests were often expected to keep track of the heavens in this sense. The word for this 'Tian', is opposite of Earth, Tu. Tian can also be found among the western mountains of China, in the Tianshan range upon which Kyrgystan and Xinjiang sits. The translation of this would be 'Heaven Mountain.'
Although I use the word Taoist, truly this refers to a development of earlier religious-astrological systems of thought , Taoism being the third iteration. These thoughts and ideas stem back to the I Ching, and the authors of that book - King Wen of Zhou and his son the Duke of Zhou - also often talk of 'reading the heavens' through a system of 64 trigrams. Each trigram corresponds to a six digit binary of either solid or broken lines. In order to divine, first the state of being is suspended between 'Heaven' and 'Earth'. To do this, if using the 50 yarrow sticks method, which became common, one would remove a single yarrow stick from the 50.
This represents 'Man', the suspended being between earth and heaven, ground and sky. Then the remaining odd 49 are divided randomly. Then, the right side is divided by six. The remainder represents the first Hexagram. Then, another Hexagram must be retrieved by repeating the entire process. The difference between the two lines is regarded as the 'change', having been determined by the diviner's target's fate between earth and heaven.
The two hexagrams are assigned meaning by matching them to King Wen of Zhou's 64 Hexagrams. The Duke of Zhou's role is to explain what this change represents. Finally, Confucius wrote a commentary on the I Ching, as did many, telling what exactly the two royals were talking about. The version of this book that I have further then has a Taoist master translating these three historical characters into modern English terms, for they are very cryptic.
The crypticness is intentional, as this was formerly the practice of the Taoist priesthood only. So the Mandate of Heaven, in this system of Taoist thought, would refer to fate derived from the sky, or essentially a Chinese version of the divine right of kings. When the Mandate of Heaven is lost, this represents a change - one even depicted withing the 64 Trigrams - so the people using these terminologies are using Taoist ideas about change to define political events. There is no pantheon. Heaven is the sky itself - although, sects can further adopt Gods of their own, often modeled on famous ancestors.
If I am in error anywhere please correct me, but if you have questions feel free to ask. It is a somewhat esoteric concept centered on the I Ching itself, further expanded by the Tao Te Ching by Lao Tzu (from which the name of Taoism originates). Although China includes Confuscian and Buddhist ideals as well, the Mandate of Heaven referred to in Chinese history is explicitly a Taoist concept, with Taoist priests to validate these things to Chinese rulers.
Source: I Ching by King Wen, Duke of Zhou, with commentaries by Confucius and Alfred Huang, with extrapolation by Tai Chi Quan instructors, all Taoist in nature. Tian is also a direction in the Bagua. BaGua means Eight Directions, and in terms of the cardinal compass there are two iterations of cardinal designation - former Heaven, said to be made by mythological Chinese Emperor Fu Xi, and later Heaven which was introduced after this and corresponds to Ba Gua today. Both Tai Chi Quan and Ba Qua Quan are martial arts that incorporate this concept of Heaven - Tian.
Historical China did have a pantheon, it was just a highly changeable pantheon of immortals, rather than gods in a western sense. "Heaven" was a place for those who had attained immortality, either by finding enlightenment or "the Way", or by more mystical means. The Yellow Emperor was one of these. The Yellow Emperor was the mythological ancestor of the Chinese people, who reportedly reigned for a hundred years before gaining immortality by eating jade. He's also considered a Daoist deity. He shows up as "the Emperor of Heaven" in many of the popular stories, like Journey of the West.
Actually, Journey of the West is a perfect book to read to illustrate the mythological concept of Heaven, as quite a bit of it takes place there. Monkey is looking for immortality, and he gains so much power and causes so much trouble on earth, that the Emperor of Heaven (also translated quite often as the Jade Emperor) invites him to Heaven in order to keep an eye on him. Heaven is portrayed very like an imperial court.
