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The Premier Ball is an item used to catch wild Pokémon that appear in tall grass, and other places in the wild. Currently, the engine uses the regular Poké Ball icon, but it is usually an all white Poké Ball, with a red center band, instead of black.
The catch rate is the same as the Poké Ball, (1x catch rate), with the only difference being the look of the ball.
The Premier Ball is automatically added to your inventory after purchasing 10 Poké Balls at once, at any Pokémart that sells them. It cannot be acquired any other way, and there is no limit on how many you acquire this way.