Sci-fi and Fantasy author Kate Elliot has a fantastic post up today about the skills that her protagonist has and why. While I do not doubt that it's useful stuff from the perspective of writing, it is lightning in a bottle on the topic of skills in game design. You should go read it. I would rather you go read it and skip this post than the reverse. It's that useful.
For those of you ignoring my advice, the short for is this - the emphasis of the post is on the importance of sewing to the protagonist of her novels (which I have not read, but now will on the strength of this post). This protagonist sounds like very standard fantasy hero material - swordsmanship, sharp wits, stuff like that - and sewing is a fairly anomalous skill in a heroic context, yet Elliot makes the case for why it's very important.
The reasons for this translate wonderfully to an RPG context, and I'm going to lay out three bigs ones right here.
1. Every Skill Tells a Story
In Elliot's post, the reason the protagonist knows how to sew is tied tightly to her upbringing and the social and economic situation she was in. It's opens a window on many other elements of her character.
In many RPGs, these hooks are explicitly called out (in the form of things like aspects), but there is no reason that skills can't carry a lot of that weight on their own, so long as someone stops to think about them. It's a little bit more indirect than having the player hang a lantern on the character's background, but it tends to feel very organic and fits the character very well because it's driven by choices that the player has made (with their skills).
How to use this in your game:
The fact that your game doesn't have "indie" mechanics is no reason characters can't have rich backgrounds tied to the setting. Go through a character's skill and use them as a basis for conversation. Find out how and why they learned the skill and perhaps where they learned it and from whom. Look for skills that are particularly high, particularly low, missing or out of place. Even if the player hadn't thought the background elements through when picking skills, this kind of focus questioning can really spark people's creativity.
2. Every Skill is a Social Skill
In Elliot's post, one key element of sewing is that it is a largely social activity, performed in groups and forming the basis of a lot of interaction.
If you stop and think about it, this is true of many groups. Think about your own life and consider how many of your social interactions are driven by "social skills" versus those driven by common interests and practices (which social skills are then layered on top of). True, fandom doesn't map 1:1 to a skill, but the idea is a potent one.
How to use this in your game:
Consider broadening your definition of what skills can do. Take a page from Feng Shui and allow skills to also be used for contacting people within the sphere of that skill. You might even want to more broadly allow skills to be substituted for social skills within their appropriate context, or at least grant bonuses when appealing to the group that the skill represents.
3. Every Skill is Part of the World
As an extension of skills being social is that every skill exists in the context of the larger society. This can be meaningful in a few ways. It might be economic (is this a skill people get rich off of, or which only the rich have time to learn?), cultural (is this a "woman's" skill? What about in a different group?), social (Is there a stigma associated with this skills? Is it associated with a particular group?) or logistic (Are there schools or organizations associated with these skills?). Any skill can be a window into any of these issues or ideas.
How to use this in your game
As GM, stop and consider the skill's context in the setting (and, if possible, take your cues from the player backgrounds). Ask what the "typical" person defined by that skill is like, then ask yourself how that changes from place to place.
Keep these questions in your back pocket for when players travel and you want to convey that things have changed. Describing things as looking different is one thing, but it's much less compelling then changing how the world sees the character. Even if it's just a small thing, it's personal, and that's huge.