I first became aware of the word pareidolia in a New Scientist article: "Belief special: Glad to be gullible". It immediately fascinated me and became the cornerstone of the second Bumbly book. The condition is invisible, pervasive, a blessing and a curse.
The words pareidolia and apophenia are both up-and-comers, not fully part of our lexicon, not in our spell-checkers or dictionaries; but they certainly should be.
That being the case it would be too bold for one such as I to define, but one must attempt to do so, as one did bring up the subject. Apophenia and pareidoilia are related to each other, in that both refer to the patterns, meanings and connections that we perceive in the world around us. Apophenia is a more general term where as pareidolia, I believe, applies specifically to what the senses perceive. The question of interest is whether what we see is actually there...
Here are some links I've found where others attempt to describe and illustrate the concept.