Aside from the extra experience points, you do not gain anything from an experience bomb.
The character's experience points are a measure of experience/knowledge/etc. If you defeat stronger monsters than yourself you get more experience than you would if you were the same level, while if you wait until you level up, you get less or no experience for the same creature. For a given opponent type and character level, you usually get a certain amount of experience.
In purely conceptual terms (not connected to anything in the game), if your character notices something during a fight or does something that works better than expected, they would learn more from that fight than with a similar opponent. This is not a huge revelation (like learning a new skill or getting stat points) but simply a larger amount of experience than other fights (increased experience points). The learning from your original quote is referring a conceptual explanation of an experience point bonus, not something your character actually gets.