They are comics based on Nuzlocke challenges that people have done.
A Nuzlocke challenge is when you play through one of the Pokemon games with these rules:
1. You can only capture the first Pokemon you encounter on each route.
2. If a Pokemon faints, it's dead. You must release it.
Some people add other rules to make it even more challenging, but the point is to use Pokemon you wouldn't otherwise choose and to become more attached to your team. It's a lot of fun, and tons of people make comics about their play through the game.