| It's fun to pretend
|The Twilight Zone|
Paranormal is a general term used to describe various unexplained phenomena, such as spontaneous human combustion. More often than not, paranormal activities invoke supernatural rather than naturalistic explanations — although a few sub-fields of paranormal investigation such as cryptozoology do claim "naturalistic" explanations, but these are mostly bullshit.
Bullshit or not, a large percentage of the population apparently believes in some level of paranormal activities, at least according to 2006 Baylor Religion Survey. Of course, how that relates to the belief in religion in general is debated.
 General pseudoscience
In general, paranormal phenomena are outside of what one would normally expect to observe in the real world. Furthermore, the phenomena are generally not reproducible under controlled conditions and it is therefore not possible to investigate them using the scientific method. For these deep-seated reasons (among several others of equal hinderance to the "believers") paranormal phenomena are per definition classed as pseudoscience.
However, many of the legitimate scientific investigations that have been made into paranormal activity have turned up interesting results, although most, if not all, turn out to have naturalistic explanations. Ghosts for instance, can be explained by minor hallucinations that have been replicated in labs. The 'spooky' or 'sickly' feeling of walking into a haunted house has been replicated by using very low frequency soundwaves. Acts such as fortune telling or talking to the dead can easily be replicated in controlled conditions by people, such as Derren Brown, utilising the techniques that mediums and fortune-tellers are suspected of using to dupe otherwise innocent customers (e.g., cold reading or hot reading).