"The experience explained itself to him." How can an experience explain itself? What's the irony of such a statement?
The context here is that Jonas is feeling what it is like to go down a hill on a sled. He has never before encountered a hill but he understands right away that he is going downhill. This is the experience that explains itself.
There are many things, like going downhill, that cannot really be explained in words. Most physical sensations are like that. Try describing what it feels like to take a bite of your favorite food, for example. In non-physical sensations, try to explain in words what it feels like to be in love. These are things that can only explain themselves.
The only irony I can see is that this is not usually how we use words. Other than that, I don't think it's ironic because it makes complete sense to me.
To start with the statement "the experience explained itself to him" is a personification. Human qualities are given to something that is non-living.
If one thinks about it, no one else has had any of the experiences in their lives. Even Jonas has never had experiences that were not controlled. In the book the statement was made relative to Jonas first trip on a sled. If a person has never ridden a sled it would be hard to describe what it is like. Jonas has the chance to experience it. By doing this he has felt every feeling associated with the ride. He does not just receive the memory; he participates in the memory so it can become his memory. (Chapter 11 page 81)
The irony is that although he remembers the experience as though it had really happened it had never really happened to him.