For me, after I have had an experience the feeling part of the experience starts to fade.
I can remember that I experience something exciting, or breathtaking, or insightful, but being able to relive the feeling becomes harder as time goes by.
Photography captures the feeling of the experience so that I can relive the experience later.
Being able to relive those experiences also lets me re-experience the affect of those experiences.
Experiences that are awe-inspiring induce inspiration. Being able to obtain that boost of inspiration at a later time results in a more fulfilled life.
We seek out experiences to be moved, to be fulfilled, to be inspired. Photography allows me to re-experience those experiences and thereby get to be moved, fulfilled, and inspired again.