The important work for which they have received the prize is their contribution to modelling expectations. Prior to their work economists used a method known as 'adaptive expectations' to predict how households and firms would react to policy changes. This meant the computer models of the time used an equation that implied expectations moved slowly after a change in policy or events. Without being too technical this meant that policy changes could have big effects on behavior even though the policy was very predictable and mechanistic.
Sargent and Sims showed that expectations changed faster than previously thought and that by manipulating the expectations of firms and households policy, say to reduce inflation, would be much more effective. Many of you will have already looked at the importance of inflation expectations in the inflation process.
Today their work is very important in deciding macroeconomic policy, particularly in designing monetary policy. Take for example the debate on the pace of deficit reduction. Confidence is crucial in consumption and investment and based on their work it could be argued that more public spending and higher budget deficits will actually cause a worsening of confidence due to the effect it has on the expectations of households and firms.
The Nobel website has a Popular Information section, look at the 'Information for the Public' link and that allows you to download an excellent, non-technical, summary of their work. (Pretty important for anyone considering Oxbridge/LSE/Warwick/Southampton/UCL economics.)
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