When I talk to my wife about going for my 'next degree' or meeting a new initiate, these words roll off my tongue quite easily, yet my wife looks at me with a puzzled expression, an expression I soon adopted, when I asked myself "What is initiation?".
Initiation in its simplist sense - is being shown something by someone 'in the know', taking this in an operative masonic sense, it was being taught geometry by the tools of the trade, creating something solid from abstract ideas (this is the real understanding of the term magic - not most tosh spouted by occultists).
As Dr Lomas says:
"If your level of perception could be changed, if you could be raised up in awareness and understanding things in the upper world"
(The upper world in this instance meaning - opening intellectual and spiritual awareness beyond our current parochial climate.)
Initiation can teach you that there is infinitely more 'out there' than you know currently, it gives you a taste that you can explore uncharted intellectual and spiritual waters through reason and intellect. It gives you the tools to earnestly explore the inner nature of YOU and how you can become a more 'rounded' individual.