One of the most powerful educators in a person's life is experience. When someone gives advice that they stand firmly behind, they frequently say, "I speaketh from experience." Many people define "experience" as events that have happened to them.
However, two people can live through identical events and come out with very different takes on the "experience," and having learned very different lessons. For example, two baby-sitters baby-sit a kid who is described by their peers as a "nightmare." Both of them sit the kid, and he shows all his mettle to each sitter. One sitter comes away believing that the kid has earned his reputation, and never sits the kid again. The other sitter comes away believing that you just have to know how to handle the kid, and sits the child multiple times afterward.
Aldous Huxley takes this disconnect and develops a different definition of experience; "...what a man does with what happens to him." Huxley's emphasis is that the individual determines what they will learn from an experience. In the example, the first sitter let the failure of her first attempt be the lesson taught; i.e. never try to sit a kid like that again. The second sitter let the nuances of the first attempt inform her of what positive and negative reinforcements worked on the kid, and that enabled future success.
We can let the experience of success and failures paint with broad strokes, or we can analyze what worked and didn't work in each experience, and let that inform future ventures. That seems to be Aldous Huxley's message.