Well, who better to explain than Professor Chris French!

Anomalistic psychology may be defined as the study of extraordinary phenomena of behaviour and experience, including (but not restricted to) those which are often labeled "paranormal". It is directed towards understanding bizarre experiences that many people have without assuming a priori that there is anything paranormal involved. It entails attempting to explain paranormal and related beliefs and ostensibly paranormal experiences in terms of known psychological and physical factors.

http://www.gold.ac.uk/apru/what/
In essence, anomalistic psychology attempts to explain peculiar belief and experience (not necessarily paranormal belief) through what we know about psychology, neuroscience etc. In other words, it is a truly scientific approach to investigating such phenomena (building testable/falsifiable theories that are built upon previous scientific theory).

If any approach is likely to explain what paranormal-type experiences really are, then this approach (IMO) is it.

For more of an introduction to anomalous psychology, see Chris in The Guardian: http://www.guardian.co.uk/science/20...tical-thinking