A Pokeball is a small ball-like object in the Pokemon shames that is used to catch Pokemon by cramming them in there. Because of this, some people had a controversy about animal abuse in the Pokemon World. There are many types of Pokeballs, like the rare Master Ball, yet there's usually just one in each game. However, you can have unlimited Master Balls if you have an Action Replay thingie. As shown in the anime and shames, one Pokemon Trainer can only carry up to six Pokeballs. However, because of what boxes do to Pokemon some trainers carry around illegal ammounts of Pokeballs, especially if some of the Pokemon are Mudkipz.
The fact Pokemon have to stay in these leads to thought of animal abuse, as they really don't know what it's like in them. However, Doctor Tree name reveals to the public that what's in these are what it looks like if you look into it. Once Ash got trapped in one, and he escaped when his Pikachu attempted to destroy it.