Non-dualism implies that things appear distinct while not being separate. The term can refer to a belief, condition, theory, practice, or quality.
Non-dualism can be seen as the belief or understanding that dualism or dichotomy are illusory phenomena. Examples of dualism would be self/other, good/evil, etc. A non-dual philosophical or religious perspective maintains that there is no fundamental distinction between mind and matter, or that the entire phenomenological world is an illusion (with reality being described variously as the Void, the Is, Emptiness, the mind of God, Atman or Brahman).
Non-dualism can refer to the quality of union with reality, or God, or the Absolute. This quality is knowable and can be gained spontaneously and via practice of inquiry. Non-dualism generally manifests in the religious and philosophical beliefs of eastern religions, but isn't a non-Christian philosophy. The God of traditional Christianity is absolute and infinite. The devil or adversary is an opposing character, but is subordinate to God. The Christian faith thus does not consider the duality of good and evil to be two equal and opposing forces. Mystical Christianity can be entirely non-dual, as in the teachings of Meister Eckhart, or St. John of the Cross, among others.
"A Course in Miracles" or ACIM is a modern day Christian non-dualistic teaching. This tradition states, "Nothing real can be threatened. Nothing unreal exists. Herein lies the peace of God." Christian Science might also qualify as non-dualistic.