Tathāgatagarbha, also known as Buddha-nature, is a concept that is central to Mahayana Buddhism. It is considered a core belief in the sense that it is a fundamental aspect of the teachings of the Buddha and is present in many Buddhist scriptures and teachings.

At its core, Tathāgatagarbha refers to the potential for enlightenment that exists within all beings. It is believed that every being, no matter their past actions or current state, has the potential to attain enlightenment and become a Buddha. This belief is rooted in the idea of the ultimate nature of reality, which is seen as pure, perfect, and unchanging.

This concept is closely related to the Mahayana Buddhist idea of the bodhisattva, someone who has dedicated themselves to attaining enlightenment for the benefit of all beings. The bodhisattva's journey is seen as a path towards realizing their own Buddha-nature and helping others to do the same.

Tathāgatagarbha is also considered a core belief because it is seen as a unifying principle in the diverse teachings of Mahayana Buddhism. It is a way to understand the various teachings and practices as all aiming towards the same goal of realizing one's Buddha-nature.

Furthermore, Tathāgatagarbha is often seen as a counter to the concept of anatman, or the idea of no-self, which is a fundamental concept in other Buddhist traditions. While anatman emphasizes the lack of a permanent, independent self, Tathāgatagarbha emphasizes the potential for enlightenment and the inherent qualities of the mind that make enlightenment possible.

However, it is important to note that Tathāgatagarbha is not considered a core belief in all Buddhist traditions. Some schools, such as Theravada Buddhism, do not place as much emphasis on this concept and may even reject it as being incompatible with their teachings.

In conclusion, while Tathāgatagarbha may not be considered a core belief in all Buddhist traditions, it is a central concept in Mahayana Buddhism and plays a significant role in understanding the nature of reality, the path to enlightenment, and the potential for all beings to attain Buddhahood.