It's a very good -- and hence complicated -- question. The answer is "yes, just a little bit, sometimes." :)

A stock's price is a reflection of what investors expect its future profits to be. If the price is high, then expected profits are high. If it's low, then the expected profits over time are low. So seeing the price of stocks decline means that investors believe that corporate profits are going to be smaller than they thought. Profits could drop for several reasons. First, it could mean that the economy could be bad: a poorly performing economy isn't going to support fast earnings growth, because no one is buying goods and services. Alternately, it could mean that investors expect businesses to see a lot more competition. This is extremely good news for the whole economy, because competition forces businesses to be more efficient, but bad news for shareholders, who would prefer profitable niches with little competition.

Stock prices also have some weak feedback effects on the broader economy. First, businesses need capital to grow, and raise that capital on the stock market. A bad stock market means that investment banks and venture capitalists aren't going to be willing to fund as many startups, which will slow the pace of innovation a bit. The reason this is only a weak effect is that there are plenty of other ways to raise capital, like bank loans and corporate bond offerings. Second, there's the "wealth effect". People who see their stock portfolios rise have more money to spend. This is only a weak effect because wages are a vastly larger fraction of wealth than stock portfolios.

So a stock market decline is moderately bad news if the economy is already doing poorly. It hardly signifies if the underlying fundamentals are sound. In the current economy, I think that the decline doesn't matter too much. We have had very solid GDP growth so far this year, and absurdly huge increases in labor productivity. Together, this suggests to me that the decline in the stock market is not a big deal: right now it's mostly just a sign that investors are getting realistic about future profits. But if the recovery sputters out or unemployment rises, though, then it will be a serious cause for concern.