I would say its an inquiry into the nature of your conscious experience, using meditation. Most meditation seems tied up with religion to greater or lesses extents. Sam Harris tries to do away with that.

Some people have already posted his insight meditation which is worth trying. (Maybe try a bit of more basic breathing meditation first so you realize how distracted you are getting with your thoughts before trying - you will likely get a lot more out of it if you can keep your mind from jumping around).

I would say the difference with psychology is that psychology is based on external observations and predictions, while "spirituality" is your own internal experience. They are completely different.