There are natural and spiritual realities. We can get some idea of them if we think of them as planes of existence, or different dimensions, or worlds.
From our natural world perspective, we get glimpses, sometimes, of an inner, or as Swedenborg describes it, a prior, reality. Sometimes it comes around the time that someone we know is dying. We see them interacting in a very real way with people who have died already. Sometimes there is a near death experience, where someone experiences a spiritual world, and then is drawn back into this one.
There's a long tradition, too, in many many cultures, of dreams being sought, and interpreted. In sleep, sometimes, the boundary between the physical world and the spiritual world seems to thin.
(References: Conjugial Love 329)