In addition to the great answers here, "gaining visibility" IMO, is much more than the end result of being the popular kid in school. It encompasses skills you'll inevitably acquire the route to being loved by good, feared by evil:
- Communication skills
- Interpersonal relation skills
- Conflict resolution
- Office/Organizational etiquette
- Adaptability
The journey to being a known brand in any shop will undoubtedly require you to have a grasp of these skills. Unless you've resigned yourself to a future of being the Milton Waddams of your shop, you'll eventually need to get your name out there and mix with people. Depending on the size of your organization, your relative obscurity might hurt you moving forward. Sure you bang out great code, but it'll be all too easy for your work to get lost in the deluge in a large organization. Or worse, someone else could steal your shine (or outright take credit) for your work. And no one would care, because they don't know who you are.
If you love your job and enjoy the action, you should at least, be willing to position yourself as the go-to guy for certain things. That'll pull more action your way. Even if you decide you're going to stay above the fray of office politics, your visibility will guarantee that you're getting bigger and better projects. Squeaky wheel gets the grease, they sometimes say