The credit rating assesses a country/company's/individual (C/C/I) risk of not repaying any debt they may have. The methods of calculating this are arcane but include present indebtedness, likely future indebtedness, ability to service debt and a number of other quantative and qualitative factors that may affect a C/C/I ability or willingness to pay its debts.
In theory when a C/C/I has their credit rating reduced the interest they are charged for any further borrowing by other C/C/Is will go up to reflect the increased risk of default on the debt and borrowing may be more difficult. In a national situation this can lead to higher interest rates in the economy with all the bad/good effects this can have, companies paying more for business loans to invest in capital projects, which may mean urgently needed and productive manufacturing investments aren' made, harming the economy long term or even leading to some companies moving to a lower interest economies, leading to job losses, mortgage rates go up but of, course interest rates on savings rise, which is a plus for some.
In fact a minor downgrading like this is unlikely to have any significant effect on the UK. Other countries in the same situation, which I think include the US, seem to find that the reduced credit rating has no real effect on anything. However should if fall to A, or heaven forfend BBB, then the s**t really hits the fan.
In the meanwhile, it is a slap across the wrist for Osbourne, who has until now been able to boast that there is international approval for his policies because we have kept our AAA ranking while other countries in a similar situation have lost theirs because they are not considered to have economies as well managed as ours in the current situation. Well we now join the list of countries whose economies are not considered as well manages as they could be.