Have you ever noticed how characters in science fiction and fantasy seem to have superpowers? I'm not even talking about the superhero type. I mean special skills - things that nobody else can do, that usually make these people indispensable to the plot. To pull from David Eddings, maybe one guy can steal anything and speak a secret sign language, maybe another can turn into a bear, maybe another never gets scared, etc. The nice thing about Eddings' characters is that he usually has a personal history for the character which explains their terrific strengths (and peculiar weaknesses).
This is really important.
A character who can do unusual things is really great, even if it's something as subtle as being graceful in movement. But without grounding, those special skills can seem arbitrary. When you look at actual superheroes, one of the coolest things about them is that they have special origin stories. Even the X-men's relatively arbitrary powers are grounded in a general tendency for human mutation.
So think through how your character got to be this way. Does she fight well because she was trained in kung fu? Does he have strong arms because he was apprenticed to the blacksmith? Does he know about lightspeed physics because he's a professor, or the ship's engineer? Does he know about linguistics in spite of his young age because he's the son of a famous linguist?
One of the things I always enjoyed about the character Pazu from Miyazaki's film, Castle in the Sky, was that he was a miner. As the movie starts, you see him hefting heavy weights and crawling all over (and repairing) these massive steam engines that bring the miners up from the tunnels below. You also see him being comfortable in dark tunnels - and all this seems perfectly natural. Then later when he's volunteering to repair the engine of a pirate's airship, climbing like crazy over the outside of the actual castle in the sky, and running through the dark tunnels inside it, you have no problem with any of it. You've seen him do it before, and it all works.
This is one of those instances where you can make your world personal. Think about your character's educational background. Is it based in experience? What kind? Is it based in institutionalized education? What kind of people does your character admire as mentors or teachers, and why?
You can even take it a little further - ask yourself what ideologies might come along with your character's experience or education. Was the master abusive, inadvertently teaching hatred of his social group? Did the teacher rescue the student from poverty or some other social situation, leading the student to adopt similar social views? Did the institution teach larger social values, or the values of the particular social group it serves?
Explore the possibilities.