"To appreciate the experience" means to recognize and value the enjoyment, learning, or significance of something that you have gone through or witnessed. Full definition
For a number of participants their couple relationship had become two individuals living very different lives, with each unable to fully appreciate the experiences of the other. (interpersona.psychopen.eu)
You don't want to sound that you did not appreciate the experiences you had, but at the same time you want them to know why you have to leave. (template.net)
I'm taking a group of American students for a Parisian chocolate experience and want to make sure they can fully appreciate the experience. (davidlebovitz.com)