The purpose of meditation and prayer is to quiet the human neural circuits that keep us from approaching the experience of oneness and transcendence that other mammals achieve so easily.
Neuroscientists have located important circuits in the brain stem of humans that are crucial to spirituality and religious belief. Surprisingly, it was often thought that particular networks in the frontal cortex would be the basis of spirituality--not the brainstem.
All mammals have these brainstem circuits and thus should have some awareness of a oneness with everything or a sense of the transcendent. Further, the human prefrontal cortex and linguistic circuits interfere with connecting to oneness/transcendence and give animals a distinct advantage.
Non-humans mammals are more spiritual than we are.
Link to relevant neuroscience article.