Tathāgatagarbha, also known as Buddha-nature, is a concept in Mahayana Buddhism that refers to the inherent potential for enlightenment within all sentient beings. This concept has been interpreted in various ways by different schools of thought within Buddhism.

One interpretation of Tathāgatagarbha is that it represents the ultimate nature of reality, which is pure, luminous, and free from all defilements. This view is held by the Tathāgatagarbha or Buddha-nature school, which sees Tathāgatagarbha as the true nature of all beings, obscured by delusion and ignorance. This school emphasizes the idea that all beings have the potential to become Buddhas and achieve enlightenment.

Another interpretation of Tathāgatagarbha is that it is the innate Buddha-nature present in all sentient beings, which is obscured by the defilements of the mind. This view is held by the Yogācāra or Mind-Only school, which sees Tathāgatagarbha as the fundamental nature of the mind, which is pure and free from all conceptual constructions. According to this interpretation, the goal of practice is to uncover and realize this innate Buddha-nature.

The Madhyamaka school, on the other hand, sees Tathāgatagarbha as a provisional concept, used to point to the emptiness of all phenomena. According to this view, Tathāgatagarbha is not a real entity, but rather a skillful means to help beings understand the true nature of reality. This school emphasizes the emptiness of all things, including the idea of a permanent, inherent Buddha-nature.

The Tathāgatagarbha concept has also been interpreted as a response to the criticism that Mahayana Buddhism was too focused on emptiness and lacked a positive view of human potential. In this interpretation, Tathāgatagarbha represents the compassionate aspect of the Buddha's teaching, which emphasizes the potential for all beings to achieve enlightenment.

Finally, there is also a controversial interpretation of Tathāgatagarbha as a form of essentialism, which sees Buddha-nature as a permanent, inherent essence within all beings. This view has been criticized by some Buddhist scholars as contradicting the teachings of impermanence and no-self.

In conclusion, Tathāgatagarbha has been interpreted in different ways by different schools of thought within Buddhism. While some see it as the ultimate nature of reality, others view it as an innate potential within all beings. It is a concept that continues to be debated and explored within Buddhist philosophy and practice.