Q: However, dualism contradicts the law of conservation of matter and energy, one of the cornerstones of physics. とはどういう意味ですか?
A: 'However, dualism goes against the law of conservation of matter and energy, one of the key features/aspects of physics.'

This is a very hard sentence to understand, especially if you don't know what 'dualism' and 'law of conservation' are. But I hope that this simplification clarifies it at least a little bit.
Q: dualism とはどういう意味ですか?
A: This usually means "dual-natured", but it's a noun.

For example:
An effective sword is dual-natured, in that it must be both light and strong. This dualism is difficult to achieve.


Q: dualism, duality を使った例文を教えて下さい。
A: I don't think I've ever heard "dualism" used outside of a philosophical context. "Duality" is also very abstract, so I can't really think of a more concrete example... anyway:

Descartes' philosophy includes the idea of mind-body dualism.

Carl Jung uses the term "duality of man" to suggest that humans have two different sides.