Stock price is an indicator about the health of the company. Increased profits (for example) will drive the stock price up; excessive debt (for example) will drive it down.
The stock price has a profound effect on the company overall: for example, a declining share price will make it hard to secure credit, attract further investors, build partnerships, etc. Also, employees are often holding options or in a stock purchase plan, so a declining share price can severely dampen moralmorale.
In an extreme case, if share prices plummet too far, the company can be pressured to reverse-split the shares, and (eventually) take the company private. This recently happened to Playboy.