Bear in mind that there are more than four dimensions so whatever theory we expound to explain what the fourth dimension is must take in them all.

Here is an example of a 4-dimensional object or form:



Objects or forms such as this can be viewed and perceived directly when we are in an altered state of consciousness, such as meditation or dreaming; at these times our mind is operating in 4D mode. However, when we return to waking consciousness we no longer have a conception of what the form or object is really like because we cannot conceive it when our mind is functioning in 3D.

Artistic, creative people such as graphic designers seem to attempt to reproduce 4 dimensional objects in the logos etc. of their clients. This 4D ring is an example. One only has to look at a number of company letterheads to come across one which attempts to depict a 4D object.

Presumably the designer has seen this object, e.g. in a dream, although he may not consciously remember this when he does his design.

Really the best way to know what 4D is, is just to note those occasions when we dreamed of an interesting object but then, on waking, we seemed to "lose" it as our mind faded across the boundary from 4D to 3D.