This has been differently defined by the two great schools of thought.
All religions, says the idealist, are the efforts, poor or noble, conscious or blind, to develop the Idea of God in the soul of man.
No, replies the rationalist, it is simply the effort of the human mind to frame a Theory of Things; at first, religion is an early system of natural philosophy; later it becomes moral philosophy.

Explain the Universe by physical laws, point out that the origin and aim of ethics are the relations of men, and we shall have no more religions, nor need any.
The first answer is too intangible, the second too narrow.

The rude savage does not philosophize on phenomena; the enlightened student sees in them but interacting forces: yet both may be profoundly religious.

Nor can morality be accepted as a criterion of religions.

The bloody scenes in the Mexican teocalli were merciful compared with those in the torture rooms of the Inquisition.