When I engage in serious prayer, it's usually for focusing inward on what I need to improve about myself. "Need to" because I will burn in an eternal fire if I don't? Well, personally no. I tend to think that disappointing myself and ending up in disastrous situations that I know I could have avoided, and are therefore my fault, is kind of like a "lake of fire" punishment. It sounds a little melodramatic when you say it that way, though.
You will notice that this basically amounts to a little "strategic planning session". For me, I guess that's what it is, dealing mainly with emotions and motives instead of numbers. Since that introspection is a strategy session for the most basic and fundamental pillars of my life (that's what prayer concerns, things like emotions and motives), it is important and meaningful enough that I may call it "spiritually fulfilling".
I'm not really sure myself. I tried to describe it, so this is somewhat close.
Edit: Maybe you could say that prayer is my N-time? Time that I privately devote to studying the big picture...that sounds right. That's how I treat "prayer", anyway. I just made that connection...