Under rational expectations, it is assumed that actual outcomes do not differ systematically or predictably from what was expected. That is, it assumes that people do not make systematic errors when predicting the future. In an economic model, this is typically modelled by assuming that the expected value of a variable is equal to the value predicted by the model, plus a random error term.
Rational expectations theories were developed in response to percieved flaws in theories based on adaptive expectations. Under adaptive expectations, expectations of the future value of an economic variable are based on past values. For example, people would be assumed to predict inflation by looking at inflation last year and in previous years. This means that if the government were to choose a policy that led to constantly rising inflation, under adaptive expectations people would be assumed to always underestimate inflation. This may be regarded as unrealistic - surely rational individuals would sooner or later realise the government's policy and take it into account in forming their expectations?
The hypothesis of rational expectations addresses this criticism by assuming that individuals take all available information into account in forming expectations. Though expectations may turn out incorrect, the deviations will not deviate systematically from the expected values.
The rational expectations hypothesis has been used to support some controversial conclusions for economic policymaking. The hypothesis is often critised as an unrealistic model of how expectations are formed.