Pension- and many "low-risk" investment funds may only invest in AAA-rated stocks and bonds. While the S&P rating alone doesn't imply that such funds must immediately disinvest in US bonds (Fitch and Moody's are holding), it does create the risk that the other rating agencies will follow suite and also lower the US rating.
As the largest issuer of bonds, controller of the world's reserve currency, and with many emerging markets placing almost all their current account surpluses in US bonds, this risk change has implications everywhere.
Some companies will already start disinvestment while some investors will start demanding higher interest returns in order to buy US bonds. It isn't yet a stampede, but the gates are now open.
That said, S&P is simply reflecting the opinions of bond traders. Markets were already unstable long before the downrating. However, from the US perspective, it is a timely reminder to politicians that the global balance is shifting and that the US cannot count on incumbency to protect it from the disapproval of financial analysts.