Directly it doesn't really affect the company at all. Its used if the company wants to raise some money so it issues new shares and sells them to the market or if the owners of the company want to make some money. The directors/executives of a public company want it to do well since their bosses are technically the owners or the shareholders so if they do badly, they get fired. And they're given extra incentives in the form of stock and stock options.
Or at least this is how I think it works.
mmm, doughnut
-Homer J. Simpson